UA does interline at SIN, even if you hold a separate ticket on a different airline. But if your Garuda flight is a certain number of hours after your United arrival (I'm not sure how many hours that is), they won't interline. We've had bags interlined from UA to SQ, even with a seven-hour layover.

UA can't check you in for your Garuda flight. There are connections desks in all of the terminals. At the Terminal 1 C Concourse (where the United flights arrive), there is a connection desk on your right as you leave the gate area. If your flight is leaving soon after you arrive in SIN, you can also go to the gate your Garuda flight is departing from.

If the worst case occurs (long layover, departure gate not open yet, no Garuda agents available in the airside area), you'll have to go through Immigration to the landside ticketing desks. WORD OF WARNING: If you can't get a boarding pass until morning, don't leave airside until the landside ticketing desks are open. You won't be able to get back through security unless you have a boarding pass.