A 'common' hedge wizard - within the Rules As Written.

TL;DR: using feats to build lesser casters as well as 'simple' enchanters of common & uncommon magic items.

About half a century ago Gary Gygax said heroic classes were about 1% of the general populace. Of these heroes, casters were rare. Getting the help of a 'fighter' would be difficult but finding a wizard-for-hire might be impossible. 

If these casters are so rare, valuable and powerful not only would most services be impossible to purchase, 'common' and 'uncommon' magic items would be incredibly hard to find. This may seem like a boon to many a DM, but consider how much power player's characters would have given this level of monopoly. They would gain rapid power just staying at home enchanting magic items.

There are more questions: if there are common magic-welders, why wouldn't they level up & rule the world? Why would they waste their time making +1 swords or potions or... holy water? If just about anyone quasi-smart can become a wizard, why aren't there schools devoted to cranking out these careers much like modern-day universities? What is a 'hedge wizard' anyway... and why are they treated naught better than a mere cobbler or a blacksmith?

A 5E solution: petty casters use Player's Handbook feats

A 'variant' human was allowed a feat, regardless of class (or lack thereof).

Most monsters and even many beasts have 'feats'. Notice that orcs (aggressive), hobgoblins (martial advantage) and even goblins (stealthy) have feat equivalents, so members of their kind might take one of these feats below instead. As NPCs get benefits of their race, all variant humans could choose one of these feats as well. You could also surmise that any intelligent humanoid or monster with 4+ hit dice has a feat according to RAW 5E rules.

• Magic Initiate: This gives one 1st level spell / once a day / cast at lowest level plus two 'at-will' cantrips. So your town's mercenary-oriented 'hedge wizard' could cast Magic Missile or Sleep just once, resorting to some 'combat' cantrip until they get a long rest. This commoner hedge 'priest': may use Bless to make Holy Water yet use Light or Mending or Sacred Flame as backup.

These people could assist in construction of any 'common' or 'uncommon' items, assuming the right pattern / formula and adherence to your rule system (be that the DM's Guide or alternate Xanathar's rules). Such basic spells may keep a community running as some of the simplest of at-will cantrips can transform a village or town (examples below).

• Ritual Caster: This gives a whole bunch of 1st, 2nd or even 3rd level spells pending the level of the NPC - though such spells are difficult to use in combat. This explains how that ancient crone has access to mind-blowingly powerful Contact Other Plane - yet inability to launch Fireballs to save her village. This also gives a reason why anyone would use the much-reviled Skywrite spell - communication between villages in a medieval fantasy would be beyond price.

Look at the lists of cantrips, 1st level spells or any sets of ritual spells. Such 'hedge' casters can provide valuable services for their community. Let us review some examples below.

Hedge Caster Spells Of Interest:

Cantrips:

• Control Flames: great for putting out fires, one 5' cube every six seconds.
• Create Fire: heats homes without fuel - a 5' cube is enough to heat a town hall
• Fire Bolt: hot enough and focused to function in a smithy
• Gust: keep one kite (less than five pounds) in the air, up to 30' above the caster / also helps sail ships
• Magic Stone: make up to three other commoners dangerous ranged combatants up to 60' range
• Mending: fix all broken, ripped and shattered items in a town
• Message: relay or send silent information to allies in range
• Mold Earth: construction, landscaping and a printing press palate
• Prestidigitation: instant laundromat & flavour food / drinks
• Shape Water: instant cooling / ice cream manufacture / molding shapes / turbine engine / many more
• Spare The Dying: lifeguard life saver

1st level:

• Cure Wounds: able to help make uncommon magic items that heal.
• Detect Evil &/or Good: Got demons? Find out!
• Entangle:
• Goodberry: heal large numbers of trivial wounds
• Sleep
• Silent Image

Ritual spells present a smaller list but can be cast much more often:

• Ceremony: replace a cleric under many circumstances

• purifying rotting foods during hard times, famines, a siege - or even to help an ally

speaking with local animals, allowing fishers or pearl-divers to breathe water, using animal messengers for communication to nearby towns and even (albeit rarely) a few divination & commune spells. This would be a fantastic feat for many monsters to have as well, such as hags or Nothics that happen to have a high enough hit dice to cast the more powerful rituals.

Adventure Ideas - Pick Up & Go:

• A group of kuo-toa using shaped water needles to inject oyster-clam type creatures with bits of their shells - creating thousands of different pearls of all coloured, varieties and sizes. This attracts the attention of many other treasure seeking creatures, up to and including dragons.
• Orcs have been using mold earth to power many power hammers. Molded earth also helps to create sand molds for many objects they need for their armies. With the help of a surprisingly mechanically inclined tiefling-orc, they are building strange shield guardians to help in the speed and efficiency of their attacks.
• A group of dryads have been using divination and speaking with animals to find weaknesses in local hag contracts, covenants and power-dealings. Their meddling has summoned their ire and they need help!
• A dying town sends a number of Skywrite messages and goes silent. Hidden in the messages are clues to break into the town and save them all from slavery. Turns out that the town had a number of secret weapons that they did not have the time nor manpower to utilize - perhaps someone else can?
• A surprisingly nasty bard travels with a troupe of entrepreneurial creatures, surprisingly good at entertaining. They also take far more than they give, often in the shape of enslaved people rather than stolen treasure. Hidden in this master bard's loot is a treasure 'map' consisting of magical mouths that all require special triggers. Unlocking this Map of Mouths will not only reveal all the secrets on how she steals people, but reveal who she works for and why. And some treasure too, for sure.
• A selfish gladiator goblin has figured out how to ritual cast spells and in contacting another plane has found secrets to an ancient and powerful artifact which he should never own. Fortunately for clever people - the 'gibberish' when such a spell is failed provides vital clues as to what this item is and where it can be found.
• A group of mist elves has a group of casters using leomond's tiny huts made of fog - before attacking they set up a few dozen as a wall-collective. Little do they know that the targets they are attacking hold hostages that need saving. You don't know how much time you have before the strikes begin, you must sneak into the enemy enclave and get the hostages to safety.
• A great noble was assassinated - fortunately she left a will. Unfortunately, this will is within Scripts of Illusion. Unfortunately, it is not clear who can read it. Fortunately, the 'cover' of this book describes a few of those that should be able to release the contents. Unfortunately this covering illusion is cryptic and these persons may be a number of days journey away. The ten day countdown commences before the magic runs out and the secrets of this will are lost forever.
• A person you know has drawn The Void from the Deck of Many Things. Unbeknownst to any of you (including this person), a ritual for Rary's Thinking / Binding was set up. The soul sends information as to where it is - including many other souls. if you can use the right teleportation magic in time you might be able to make this a speedy quest, albeit dangerous one.
• A most Gentle spell of Repose has kept a great yet horrible hero from death for centuries - a very patient sea elven group has been recasting it for ages. They came to you because this body was stolen by an elven-looking malenti-changeling threw the body (and a great weight) into the Forbidden Well. Fortunately, it is against the religion of the sahuagin to go down there. Alas, it is also against the faith of the aquatic elven to go down as well. Fortunately, the group they contact has no such compulsions (the PC group).
• A hedge-druid gets ahold of a Staff of the Woodlands. He has been cranking out all sorts of things intelligent, both beast and wooden. Though he only has six hit points he has become incredibly powerful, threatening to destroy a half-orc mining town that has been brutal to the environment. 
• A few goblins have at-will access to Mold Earth cantrip. Disaster! As a small team they can rapidly tunnel, build walls and are actually a threat to a rather large town. Their task-master, a hobgoblin warrior, is feared dead and this goblinoid mischief can no longer be contained.
• The mail delivery person for the town has vanished but his Phantom Steed keeps showing up in town looking for help. Wherever this person is being held, he or she must be less than an hour ride away. All adventurers must do to begin this adventure is to get on this horse. (Logically the first horse would vanish quickly... but the second and third horses phantom horses sent would last longer and longer as they got closer to their target-caster).
• The town elder has access to Commune With Nature. In the process of digging new wells for developing settlements ancient catacombs have been unearthed. Players suspect that this spell would have informed them of such a calamity. This means that either the mayor wanted to release this Ancient Evil - or this leader is possessed by forces both dangerous and unfathomable.
• Multiple highway bandits have access to Sleep spells. Though no one has been hurt, substantial amounts of goods have been taken. Worse, these victims are often left in the most humiliating outfits in rather compromising positions. Elves (creatures immune to sleeping effects) have coincidentally shown up to set things right. They can easily disguise themselves as humans and counter ambush these ruffians... for a fee, of course.
• Everyone knows that the army of nasty humanoids is on their way. A Divination from the nearby hag trio has suggested that there is a way to save your town, survive the siege... possibly even win the war. It is a set of cryptic riddles and someone must figure them out. Before the old girls will give up their secrets however, they require some adventurers to get some things done for them.
• A hedge-wizard, known for his or her excellent cleaning and mending, has arrived in the tavern in a state of pure panic. Turns out his Unseen Servant has developed a mind of its own and has been murdering towns folk. He or she needs proof that this magical force is acting independently. This hedge-wizard is captured by the local militia-guard shortly after this explanation and must stand trial for murder / will be hanged without PC intervention.
• The nearby town's last Skywrite messages were cryptic and made little sense. Explorers have since found all inhabitants of that area simply gone. Local militia are unable to investigate further (i.e. they fled like cowards). Can someone brave or foolhardy help out?