Consider whether the champions that you have access to have any core mechanics/innate advantages over your lane opponent (i.e. more sustain, better/safer harass, easier farming, better scaling, etc.) and weigh that against your opponent's top lane choice. Also key to consider are what your jungler is (what would assist his ganks, what does he bring to the plate vs. yourself) and what the enemy jungler is (what kind of ganks can you expect, etc.). In addition, looking at the enemy team as a whole can allow you to choose a champion that may slightly disadvantage yourself in lane vs. your top opponent but counters two or more enemy players. What's most critical about top lane is being very map aware (don't rely purely on mia calls), expecting ganks from odd routes (through lane, flashes over walls, etc.), and to be very, very self-sufficient. If you're doing it right, you can tie up the enemy jungler and/or mid in your top lane, allowing the rest of your team to push/setup plays while you hold the fort. Essentially top lane is your own island and you are Sir Winston Churchill, here to repel the Nazi menace from Europe.

Thanks for all the tips everyone!

Ban teemo and you should be fine

One big problem I have. The other day I got put against a garen that was REALLY good. I was playing Jax and he clearly knew exactly how to take me down. Not only that, but he could easily solo tower dive me at level 3 and on and get a guaranteed kill every time because I had no idea what to do other than stun him and try to jump away. But he got me every time. What could I possibly do in that situation? My jungler never came up to help me and I was stuck at my tower for the entire laning phase and couldnt even farm under tower because he could take me down to half health with 1 Q-E combo and get out with almost no dmg from tower. I kept trying to build defense against him but nothing seemed to work. That's my biggest problem, I can usually stalemate my lane if I'm down early game, but in that situation i was just floundering because I had no idea how to stop him and my team wasn't helping until it was already too late.