1 hour and 45 minutes should be plenty, if all goes well.
If you are passing through Frankfurt to and from non-Schengen countries, your transfer will take place entirely within the transit zone, which in most cases means you will not need to pass through a passport checkpoint (although not always.) You may or may not also have to pass through a security screening depending on your origin and/or destination, and there are occasionally random security checkpoints in the terminals.
If your connecting flight leaves from a different terminal than the one you arrive in, the Sky Line train will allow you to make the transfer while remaining in the transit zone.
Transfers between non-Schengen and Schengen countries (including Germany) will require you to go through passport control. Unlike many international airports with a single immigration area, you will find passport checkpoints in each of the concourses. However, you shouldn't need to seek one out-- just follow the signs to the gate for your connecting flight and you will pass through a checkpoint somewhere along the way.
If you are connecting to another flight with a short connection time (typically less than 45 minutes), you should be able to use the "Fast Lane" service at the passport control stations; eligible flights are shown on a display above the "Fast Lane" counter.
After clearing passport control, you can then proceed to the gate for your connecting flight. Be sure to check the flight information displays for the latest gate number as flights are sometimes moved to other gates due to late or early arrivals. If your connecting flight is in the other terminal, use the Sky Line train. A tunnel allows you to transfer within the Schengen zones of concourses 1/A and 1/B so that you do not need to leave the secure area; use the elevators near gates A15 and B19. There is also a passageway inside the secure zone from concourse 1/B to concourse 1/C on level 3.
If you need a boarding pass or additional assistance, check-in at your airline's transfer counter first thing after arriving.
Lufthansa advertises a guaranteed connection time of 45 minutes at FRA. However, based on experience, an hour is probably more realistic if you're staying within the transit or Schengen zones and 75 minutes if you have to cross between them. Flights from North America to FRA often arrive early, but don't count on it as any time savings gained from that strong tailwind are frequently lost due to congestion in Frankfurt's approach and landing slots.
If you have a long layover (more than a couple of hours), you might consider visiting the spectator's terrace on top of Terminal 2 where for €3 you can watch the airfield activity, or the free art galleries in each terminal. Note that these may require leaving the airside of the airport. Long layovers are also conducive to taking a quick sightseeing trip into Frankfurt-- the S-Bahn train will get you downtown in less than 15 minutes. (See information under "Arriving" above.) There is also a small transit hotel near gate Z25 where you can get some rest between flights.
For more information about Frankfurt Airport, see their official website: