When I try to get into a match, a box pops up saying:
"An unknown directX error has occured. Please make sure your video card supports shader model 2.0 and that it is using drivers from the manufacture."
How do I fix this?

What graphics/video card do you have currently?

Move to the folder:
League of Legends/Config/
Delete the file 'game.cfg' and 'input.txt'
Relaunch the game, try to spectate someone.
IF that still doesn't work, move to these two folders:
League of Legends/RADS/projects/lol_game_client and lol_game_client_en_us
Delete both of them.
Then run the repair option in the launcher, by clicking the cogwheel in the upper right hand corner.

Executor,

Click your start menu button.
Type 'dxdiag' into the field and hit enter.
When the new screen pops up, run 'x64 version' if that button or similar wording is on the bottom.
Then, hit the 'save all information' button and remember where you saved it.
Reply to this thread with the 'go advanced button' and upload the .txt file here please.