I am traveling from the United States to the UK in a few days, and I will have a checked suitcase. My layover is in Frankfurt, Germany. Since my final stop is in the UK. Will I go through customs in Frankfurt or in the UK? Also, the two legs of my trip will be with the same airline.
Assuming that you're traveling on one ticket (and, as you say, on the same airline), your luggage will be checked through all the way to your final destination in the UK, and you won't see it as it's transferred between flights at Frankfurt. [If in doubt, check that the airport code of your destination airport appears on your bag claim tag; but most check-in agents will spontaneously tell you whether the bag has been checked through].
When you arrive in the UK, collect your suitcase and go through one of the "arrivals from outside EU" lanes at customs (color-coded red if you have goods to declare, green if you don't).
This is the general procedure for all arriving flights into the EU that connect to an intra-EU flight, unless the final destination is a domestic airport without any customs presence.
For completeness (and in contrast to what someone said in a comment), you will not have to go through immigration in Frankfurt either. Since where you came from (the US) and where you're going to (the UK) are both outside the Schengen area, you don't need to leave the extra-Schengen part of the airport in Frankfurt.
(Of course, if your layover is long enough and you have a passport that gives you visa-free entry to Schengen, you still have a choice of going through immigration anyway and have a look around).