Most S-Bahn go through the Frankfurt Hbf in the underground (tief) station, several levels below the ground level. They run at 15 min intervals. Look for the green circle with a white 'S' symbol. Here is a 3D layout of the station. The S-Bahn station is below the U-Bahn station. You'll want track 103. There are other lines using that track that don't go to the airport, so be sure you take an S8 or S9.
There are also occasional S-Bahn and regional trains that leave from the ground level of the station. That would entail a lot less walking. All of them go to the Regionalbahnhof at FRA. You'll find the schedules on the German Rail website or on the mustard colored schedules posted in the Hbf.
As I remember, there are two tunnels leading to the tracks at the Hbf in Innsbruck. There are lockers next to both tunnels (the symbol is a box with a suitcase and a key).