If you're at a station without the monitors listing standby, you might want to confirm with the GA if you are on the list, though you should have been given a departure management card that printed out at OLCI. If not, check with a check in agent and they can print one for you (maybe the kiosk's will do it to - I'm not sure when you've OLCI'd). Earlier check in will give you an edge over someone else, all else being equal (i.e. status, fare paid, etc.)

If I'm planning on standing by, I usually call reservations the night before or morning of and ask about my chances by giving them the flight number of what I am looking to clear onto. They won't give you exact numbers of seats available or anything, but will generally tell you if the flight looks really full, or with several or many empty seats, or that it looks good/not good. Seatcounter is another place to get information - you have to take the info. with a grain of salt, as this lists the number of seats UA is willing to sell in each class, not how many seats are actually available. If Y = 9, there are 9 or more seats left to sell, as it gets lower than that, you could be looking at a situation where the UA might be willing to sell the seats, but will result in overselling the flight.

Note that if you standby for a flight and don't make standby on the first one, the list is supposed to be transferred to the next flight to the same destination (assuming its not what you are already confirmed on), but its always a good idea to confirm at the new gate that your name was transferred properly.