Cass is one of my favorite champions because she lanes so rediculously well. Your noxious blast has extreme range and is brutal to harass with. Use it to set up an imaginary wall vs your enemies - you can sit behind your caster minions and plug away on opponents' minions at will while hitting enemy champs if they get in range of any of your minions. This is the outside of the wall, if they come in range pick away at them. Eventually they will get frustrated and try to cross the wall and then there's no turning back. To make sure of that, drop miasma behind them (even more lethal once you have your frost scepter) - yes behind them, don't try to use this as damage but instead use it to cut off their eventual escape route. Sink your fangs in at will until they turn to run and realize they're SOL because of your puddle. If they get uppity and go for broke and try to ulte on you, you should also have your ulte at this point so it's simple to stare em down, back up a touch while still hammering them and kiss 'em goodbye.

Teamfights later on are a bit trickier but the same concept applies. Use your miasma to disrupt but stay back. Throw some noxious constantly at anyone who comes in range, but stay back. If multiple foes get in range, stare em down then let your team turn on the heat.

It is important to remember, cassiopeia wins teamfights not by killing her enemies but by not dieing.

Boots are obvious. Cass really needs an archangel's sceptor for the mana regen, mana and get it as soon as possible. Other than these two choices, the order is really up to you. The slow scepter leads to many kills / assists and has good HP for survivability. The rods of ages stack well with mana + archangels as well as hp for survivability and AP. You want to get these with time for them to reach full potential, but at the same time a liche bane is extreemely useful. The mana adds to archangels' passive, movement speed is survivability / running down prey, magic resist never hurts, AP always a bonus and the passive is extremely fun as well. If you can reach a full build you should have over 500 AP (plus consumables) and that is some hefty damage output. I actually get the highest crit in the stats endgame with this build and one point to crit in the masteries - if it goes once, it helps a TON in a quick kill. Not to mention pushing towers / minions etc.

But for the most part, archangel's staff & boots first, then pick the rest per your playstyle / opponents.