Best way to improve in LOL?

I'd say the best thing to do is to focus on micro rather than macro concerns. Trying to get a little bit better at everything at once is nice, but it makes it harder to identify improvement.
If you play adc, focus on last-hitting for a while, either in bot-stomps or real games. Try to sort out how much damage you actually do to different enemies at different levels and with different items.
If you play something with a lot of skill-shots, try to focus on leading your shots. Try picking up whatever the fast-casting thing is.
If you play jungle, sort out good ward positions and try to work on clear times.
Break your gameplay down into components and focus one at a time, and even if it takes a while to meld them together, you will see improvement in areas as time goes on. practicing and playing the game for a while is the key i guess