You have been sent back in time to the medieval age with nothing but your clothes. You have sought out a leading academic of the age. You offer knowledge in exchange for food and shelter.
How do you explain the following to him:
realize I don't speak a lick of medieval italian, let alone modern italian and starve to death
If I merely get sent back in time without my location being moved, I die in the vacuum of space. If I get sent back in time with me having the same location w.r.t. the earth, I'm in a very sparsely populated area of north america and I'm probably going to die alone.
Alright, i think the first thing would be to show him that i'm inteligent and i'm not a mad guy trying to convince him of magic.
So the first step would be talk with him about math and geometry.
Then you have proved that you are intelingent, he might even believe that you come from the future. You show him newton's mechanics and with newton's mechanics you might be able to justify fight.
Electricity you introduce him into some basic concepts of electromagnetism, show how a magnet deflects the compass, create a generator to make electricity for deflecting compass and you do a lot of experiments to show him stuff.
Light he should alredy know optics, and explaining if it's a wave or a particle will be really difficult.
Evolution you are quite fucked up because the world hasn't been fully discovered so there aren't many examples and cases to make a full study, and bio sucks.
Time, he already knows what a clock is and i'm not going to explain relativity to him.