Frankfurt Airport is around 13 kilometres or roughly 8 miles away from Frankfurt city centre.
The close proximate makes it easy to travel back and forth between airport and city with the main 3 ways of commuting being: Train, Bus and Taxis.
You will of course also have the possibility to rent a car, although this can be quite difficult to park if the place you stay doesn’t have a parking included so you might be better off with public transportation unless you also plan to leave Frankfurt during your stay.

There are two S-Bahn lines running to Frankfurt central station called S8 and S9. The reginal train station is located under Terminal 1. There are well placed signs all over the airport and it should be no problem to find. The train should take you around 15 minutes and a one way ticked costs about 4,65 euro at the time of writing and can be bought on terminals at the train station or from the info station from the RMV, the operator of the regional trains. Train are running every five to fifteen minutes depending on the time of day. At night trains go every half an hour on the weekend. Frankfurt airport also has an international train station with some trains stopping at the main station in Frankfurt, but you will be better advised sticking to the regional train station since its easy to find and trains from there going regular and in short intervals.

In front of Terminal one you will find the Regional Bus Terminal, with buses going regular, about every fifteen minutes to half an hour. Buses going to Frankfurt are number 58, 61, 62, 72, and 77. However these busses are daytime buses and going from the early morning until the evening at about 11pm – 12pm in the night you will have two daytime busses N81 and N7. Tickets can be bought buy entering the bus from the driver and the bus will take you around 25 to 30 minutes to go to Frankfurt centre. But be advised that the buses can get stuck in traffic.

And lastly there is the possibility to take is taxi, which is probably the most comfortable but also the costliest method. Taxis can be taken in front of terminal one and two and will take you about 15 to 20 minutes to go the centre. Sometimes half an hour depending on the traffic. The Taxi should cost you somewhere between 40 and 50 euros depending on the daytime.
To conclude the matter, there are many valid ways to get to the centre if you have the money to spare the Taxi will probably be the easiest to take, trains are also really convent since the go very frequently to the centre and depending on were you have to go a bus can also be a god alternative.
However, if you choose to take the public transportation I would to download the RMW App for the google play or apple store, the app lets you check connections in Realtime and will be a very big help on your trip