Steps to making frustrating champions a little less frustrating to play against.

1. Pick the champion you hate the most.
2. Play that champion in at least 5 games. It doesn't really matter if you feed a few times, just do it.
3. While you play the champion, explore the ins and outs of the champion; learn cooldowns, ratios, and limitations.
4. When you stop playing that champion, next time you lane against him, think about all those little things you experienced for yourself. Pay attention to the fact that things you struggled on the other guy probably also struggles with from time to time.

If you do this, at the very least, you'll be able to better understand exactly why some champions seem more powerful than they are and you'll be able to play around it.

For example, I just forgotten and relearned that Fiora's Lunge gets cooldown reduction (60%) for landing it on another champion. I just thought the cooldown was that low. As a result, I missed tons of opportunities to punish her because I thought that she'd just jump on me with a tiny CD. After playing her on PBE, I learned she only gets the CDR if she hits me. No, it didn't make laning any more fun, per se, but it definitely made it less frustrating and opened up windows for me I didn't know about before.