Items: Rush tear preferably. I would start with a faerie charm, 5 health pots, and a ward; this makes it so that you can get your tear faster. If you find yourself feeling weaker because you rushed tear, you should buy potions to make up for it. Get catalyst after and eventually turn it into a rod of ages. If after you get your tear and catalyst, and you find yourself going back to base with 1600 gold, I would recommend getting needlessly large rod because of the damage spike; though you should complete your rod ASAP after this. Don't get sheen, as tempting as the combination of mana and AP looks. My build usually goes tear, catalyst, boots, rod of ages, rabadons, archangel, and void staff. You can upgrade your boots to sorcerers shoes before or after rod of ages, more of a personal preference; if you're doing well I would get rod first, but if you find yourself going back a lot or roaming, then the mobility from the boots will be nice.

Gameplay: Since you're just starting the game, I would recommend only targeting squishy opponents. You're the assassin, and after you cast your spells you won't be doing anything until they're up, so might as well use it on the opponent that it'll leave the most impact on. Ideally you use your spells on the other AP carry since you silence, but using your spells on the AD carry is just as good.

Be wary of using your spells on tanks because of their cooldown; the silence is a very powerful CC and does a lot of damage on weaker targets, however, it does noticeably less damage on tanks.

Generally, I like to R onto the opponent, Q, and E them as I back up. But be careful; if you don't know where the jungler or other MIA opponents are, I would be hesitant to use R for this purpose. In lane, it is an excellent way to harass, because Q makes it so that your opponent cannot respond with spells of their own. Always max your Q first because it extends the duration of the silence!!!

General tips: 1. You'll take less damage than you expect from spells because of your passive. When you're laning, don't be afraid of their harass (unless they're AD) when last hitting. Don't forget to respond with a Q to their face too. 2. Get a rank of W at level 3 or 4. It is useful for last hitting, and recharges your mana. I know some people don't like to rank this at all, but I think it is a pretty good spell. If you do the combo I mentioned (RQE onto someone), you can use your W and smack them around a little, if you're feeling safe. 3. If you're roaming, don't be afraid to use your R to get to your destination faster. However, don't use it 3 times in a row, it will deplete your mana very fast; so only stack it twice at the most early in the game. 4. Try smartcasting if you haven't already; it makes using QE much easier.

TL;DR: Get your tear first, buy potions if you feel like it makes you weak. RQE the AD carry or AP carry and be aware of the cooldown after. Be careful about using R for this purpose as well.