I arrive at Frankfurt international airport in the morning (9 am) and I have to wait 10 hours until my next flight. Also I don't have a visa to get out of the airport. What is the best way to get some sleep in the airport?
According to sleepinginairports.net, there are some seats without armrests in the hall between Terminal C and B, and security and cleaning staff will probably not bother you. Additionally, there are two lounges that are open to everyone (for a fee)
It's good to find a corner or a place near the wall and lay there. You can use your rucksack as a pillow, not very comfortable, but assuring, that noone would take it away. But you shouldn't be concerned about robberies in Germany. It's good to have a sleeping pad for such situations.
It's quite normal in such places, that there are a lot of people having to wait long. And some of them are tired. In case someone makes you problems, you can say you have pain in the back because of sitting too long.
Starting from March 6, 2017, there will be a hotel in the transit area (website); it is the first such hotel at a German airport. Rooms can be booked from three hours upwards, and check-in/check-out are possible at any time between 5 am and 11 pm. Considering that there are no scheduled flights during the night, this should not be a serious limitation in practice.
Rooms are not cheap, however – apparently, prices start from € 80 for three hours in a single room. Therefore, the free alternatives mentioned in the other answers may still be interesting.