Regarding the SIM-card, most of the major telcos have stores which you should be able to find at least in the city centers (not sure about FRA airport though, but you can probably find that out online). You will probably be buying a prepaid plan where the monthly fee (starting at 10 €) for data use is deducted automatically as long as you have sufficient balance. Note that German data plans normally only include a few hundred MB of monthly use, but that's not a big deal if you're only staying a few days. To purchase a SIM-card, you need your passport + cash to top up the SIM-card enough for the fee for the first month. Doing this at the telco stores is quite an easy process - ready to go in about 15 min. You could also purchase the SIM-card in other places, like the super market, but you'll have to go though the registration process yourself in that case.

Regarding directions with public transport, the local public transport coordination associations (Verkehrsverbunde) usually have excellent tools for this.
For Frankfurt (incl. Mainz): http://www.rmv.de/en/
For Munich: www.mvv-muenchen.de/en/homepage/index.html
They both have apps for minimum Android and iPhone available. Hint: some information is available in the German language edition of the websites only.