I know that you ban your counters, (ex. akali vs vlad) and champs you are unfamiliar with, but are there other factors as to what you ban, when, why, and how?
Considering it's for solo-queuing :
*Whether you're the first pick or not.
- It might be helpful not to ban useful champions (hello Warwick and Zed) if you are.
*How your team wants to play collectively (All AOE, Strong late game/early game, High CCs)
- If your team doesn't play well in late game, consider banning them. (Vayne comes to mind)
*Reading how the enemy's side ban champions.
- This is never accurate but is still useful. (e.g. banned Morgana = Leona)
A couple of ways
Ban the Flavor Of The Month champions - there's sometimes a champion which is clearly over-powered and going to be nerfed within weeks. It's usually worth banning this champion
If you're at low elo, ban Katarina... an experianced player will often pick her up, and she absolutely annihilates low ranked players who don't know how to deal with her
Ban specific counters to champions you (or your team) will be going for.
Ban counters who are a big problem to your play style. ie Vi is a nightmare for most ADC's, so if your team relies on the ADC to carry hard, she may be a good ban.