Unless you have a huge leg-up from the start, this is next to impossible.
If you arrived in 1346 England naked, with no identity, goods, money, status, and (presumably) little to no knowledge of how medieval society worked, you stand pretty much no chance of succeeding. I assume you at least speak (magically?) Middle English to talk to the commoners, and enough Middle French to at least attempt to negotiate with the nobles. Oh, and that you are at least partially immune to the common diseases of the 1300s, or you'd die of dysentery within 2 weeks tops.
The only chance you have, which is still so slim as to count as cruel and unusual torture is this:
- pretend to be a madman (easy, as they will assume so anyway).
- beg for people to give you some discarded clothing, food, and point you towards the nearest monastery (hard and grueling task, but can be done within a few months, unless the winter hits and you die frozen in a ditch)
- beg the monks to take you in. One of the many tasks medieval monks had, was running a "hospital" for madmen, orphans, curably sick, lone elderly people and hobos.
- show the monks that you can read and write (sort-of, 1300s script is VERY different from modern). Beg to be allowed to become a novice, or at least a servant in the refectory.
- manipulate your way into working in the basements.
- once you have access to the basements and the pantry, steal some old buckets and some old bread and flour. Grow moldy bread and moldy flour paste in a dark, humid, cool corner.
- procure some alkaline substances (potash, quicklime, maybe alum if you are lucky). Get some acids as well (the gall ink monks use is one, but do not get caught stealing it as it was expensive. Vinegar and sour-cabbage juice are also acidic)
- dissolve your mold into an alkaline solution. leave for a week, slowly adding acids to bring the acidity up.
- obviously fail, repeat again with different alkali, and different acids, in different proportions until you hit jackpot
- if you did everything right, the solution will form a bit of foamy scum on the surface, that might contain penicilin in random quantities, as well as a load of inert dead mold and some salts. This is your "penicilin". Drop bits of those into a spoilt puddle of sour beer: the penicilin should repel the bacterial film from forming.
- remember the recipe that worked, and repeat it several times. Should take you a year or so to perfect it.
- Convince the monks to use your "mystery cure" on a patient that looks like someone obviously suffering from a bacterial infection (septic wound, dysentery, pneumonia etc ). If they fail to listen claim the cure was revealed to you in a dream by Saint Anthony (don't tell them which St Anthony though, the confusion will help you!)
- obviously fail, repeat as many times as you can until it works or the monks run out of patience.
- IF the cure works, make sure to frame it as a great success of your Abbott, who, by God! is truly a pious and venerable man blessed by the Saints, and should lead the holy war against the demon of Black Death itself (this is also something St Anthony revealed to you in a dream).
- teach the monks how to make more penicilin. Let them perfect the process; brewing stuff precisely meticulously and efficiently was their favorite thing next to Jesus. Let them do their job, and spread the recipe across Christendom through their usual channels (which was a novice on a donkey being sent places).
- beg the monks to let you quit and retire to a cabin in the woods, where you will be meditating on the Visions of St Anthony as a lonely hermit. Stay there until the whole nonsense blows over.
There is absolutely no point in trying to achieve the same thing via secular channels. The Church, and specifically the monks, are the only people who understand the vague concept of practical science, and have the patience and curiosity to try your idea. Everybody else will dismiss you as a dimwit or a witch. Being considered a witch would not be a death sentence as one would think: the commoners were relatively ok with USEFUL witchcraft. The problem is, your brand of witchery does not conform to the common folk-medicine practice, and requires too much trial and error that the people will not accept. Besides, the commoners do not have the means to help you expand your production, and the nobles will dismiss you as an annoying charlatan. If you managed to reach the king (Edward III at that time) it would greatly increase your chances of success, since Eddy 3 was a very reasonable and practical man, if, arguably, cruel and merciless at times. But your only chance of getting an audience with the king is through the Church, because nobody else is going to vouch for you.