Am echoing
UAPremExecFlyer: it's Terminal 2. As for arriving at the check in counter, two to two and a half hours is a good time to target. Check in can be done in substantially less time if you are a UA high status flyer and you know your way around Changi Airport - there have been times where I got from curbside to lounge in 30 minutes (ie including immigration exit formalities) and spent 45 minutes in the lounge but if you're no status or UA MP regular member and flying Y, the check in for economy can be long.
Changi Airport website: pull down to UA info. Interesting they indicate check in counter opens anywhere between 2.5 to 1 hour before departure. In my experience, the 1 hour part can't be correct.
http://www.changiairport.com/en/flight/airlines.html
BTW a heads up: don't dawdle at airside if you're cutting it tight. Security check (ala TSA) happens at the gate. Don't be misled by the x-ray machine for hand carry bags before passport control.