Lbell got the gist of it. Let me add some other potentially helpful information.

United will not bump paying passengers holding a ticket if there are open seats on the airplane (even if they are first class/business/economy plus). The upgrade process is just like Lbell described (ie, no two class upgrades, based on ticket price/mileage plus status).

However, United will not put a revenue stand-by in a first or business seat. Say someone misses their earlier SFO-FRA flight because of traffic/security line/etc..., they no longer are guaranteed a seat on the next flight. They can travel as a revenue standby (higher boarding priority than retirees, employees, companions, jumpseaters). However, they can only take a coach seat. So if there is only one seat left on the airplane (first or business), and there is a revenue standby and you, you will get that seat.

Where that comes into play especially is on a foggy/rainy day in SFO where they go from 2 to 1 arrival runways. If people are flying in from SEA, PDX, SMF, RNO, etc.. to catch a connection to FRA, and their flight gets delayed due to weather, there could be a lot of misconnects. If I were you, I would try for the first flight of the day (the 747) because any misconnects/stragglers of the earlier flight can take up your seat on the later flight.

Honestly, I am willing to bet your flight goes out full in first and coach. Between 24 and 48 hours before departure, passengers can start using their miles to upgrade to first/business. So that is usually a good time to recheck the loads to see if the flight is makable. What type of airplane are you talking about that is 20 oversold. Is it the 777 or 747? On the 747, you have a chance of getting on. On the 777 flight, it is really risky. I would wear your uniform, be nice to the gate agent, and introduce yourself to the crew.
Hope that helps.