They probably already knew
It's highly likely that medieval people already knew how to make antibiotics. They didn't necessarily know it was penicillin they were making, but the history of treating wounds and infections with molds containing antibiotic substances stretches back to civilisations as old as ancient Egypt.
It's a similar case with aspirin. Although it was 'discovered' in 1899 when acetylsalicylic acid was first synthesised, people have been treating fevers with willow-bark tea containing salicylic acid since antiquity.
Considering present-day hunter-gatherer's intimate knowledge of the medicinal plants in their environment I'd guess you'd have to go back a very long way before treatments are actually a new idea.
So what can we do?
That being said, local knowledge levels will vary. What you can do is spread knowledge of these existing treatments to people who don't have it.
The other thing you can help with is refinement. One of the issues with these existing treatments is that their methods of application are limited. As previous answers have mentioned, it shouldn't be that hard to produce more concentrated penicillin and you can use that to treat non-topical infections.
Of course, the inability to adequately enforce proper courses of treatment will probably mean the advent of antibiotic-resistant diseases a hell of a lot earlier. Not certain it's such a wise long-term decision...