Well I'm no pro player, but when I start using a character I spend at least an hour in the training room practicing basic combos and looking over their respective foruma for general tech and neutral game advice.
Then I take said character into player matches and play with others until a glaring weakness in my game comes up, then I replicate the situation in practice mode until I feel as though I've mastered the appropriate response.
There's some things that you just wont predict that you'll need to learn UNTIL it happens to you. Examples include dealing with long range njp from characters like Kung Jin, how to deal with a wakeup teleport from Tanya, or how to maintain safe pressure on Reptile without eating a slide reversal.
Before Kitana had her quick mid starter reduced to 9f startup, I was having alot of trouble dealing with Jax's pressure and felt like I couldn't even press a button. I had to take the situation to the training room, replicate the frame traps, and learn both character's frame data.
Watching replays of lost matches will help alot, as well as tinkering with characters you don't normally play. Picking up Scorpion helped me tremendously in the Kitana-Scorpion matchup.
Hell you can even tackle a tower at the highest difficulty if you want to practice a safe pressure game. There's dozens of ways to up your game.