I just started playing kassadin because he fits my play style really well but still can’t figure out when or how to use his q. It says it cancels channeling abilities, what exactly does that mean? Should I be using it for the shield or the damage? It also says silence, does it actually silence?
Kassadin's Q cancels charge-up abilities like Vi Q, Nunu ultimate, Galio taunt, Xerath and Varus Q, Fiddlesticks' Drain, etc. It does not actually silence, because opponents are not prevented from casting abilities after it hits, it merely interrupts them if they are channeling an ability.
How you use it will depend on your situation.
When I'm against a poke-heavy opponent, I'll often save it so that I can fire it at minions to get the shield when I see a damaging ability coming my way. So against opponents who outrange your Q it can be used to at least absorb some of the damage you would take from their poke.
It can also be used to last-hit at a distance if it's not safe to go forwards.
It is also your only reliable way to trade with ranged opponents (especially early in the laning phase), since your E is not reliably up for every trade and your W is melee ranged. So if opponents have a similar range then you can use it on them when they try to trade with you.
Also if you're not in danger of being poked or if you're trying to build E charges you can use it to build stacks, but you should play passively and avoid trades if you do that, since it's not available to make trades if it is on cooldown.
Mainly use it for damage, shield is nice vs ap but its not that important. The silence is for a super short duration, just for interrupt channeling habilities. Channeling habilites are like 
ult, 
ult, 
ult...
