ATIS and AWOS
Before departure, listen to the ATIS (Automated Terminal Information Service), which is a prerecorded message updated every hour. ATIS gives you the current weather conditions at the airport, lists designated runways in use and any other pertinent information about the airport that you need to know. Smaller airports that don't have control towers have an AWOS (Automated Weather Observing Service) or an ASOS (Automated Surface Observing Service).
Ground Clearance
Before moving your aircraft, you need to obtain ground clearance. Dial up the ground frequency and state your aircraft call sign, position and intention, and wait for the controller to give you instructions and permission to taxi your aircraft to the runway. If you're flying an IFR (Instrument Flight Rules) flight, you'll need to contact clearance delivery before contacting ground to receive your IFR clearance.
Tower
When you are ready for takeoff, call up the tower frequency and wait to be cleared for takeoff. Only after you have received your takeoff clearance can you then move your plane out onto the runway and begin your takeoff roll. It's a good idea to double check and make sure no other planes are preparing to land on the runway that might have been missed by the tower. Such mistakes are rare, but they do occur.
TRACON
TRACON frequencies connect you with the approach and departure controllers at the airport who use radar to provide traffic control and advisories to departing and arriving aircraft. When you have successfully lifted off from the runway and have departed the airport traffic pattern, the tower will direct you to contact the TRACON controller.
CTAF
Once you're clear from the airport and the TRACON controller gives you permission to change frequencies, tune to the appropriate CTAF (Common Traffic Advisory Frequency) for your area and listen for other traffic. CTAF is the frequency that pilots use to alert other aircraft of their presence and intentions in the vicinity of smaller airports that don't have towers. You also use the CTAF to "self announce" your arrival, landing, takeoff and ground movements at any airfield that doesn't have a control tower.
Flight Service Station
The FSS frequency connects you to the local Flight Service Station, which provides current weather conditions and general information that pertains to a larger geographical area. Talk to the FSS on the ground to obtain weather briefings and file your flight plans before your flight. While in the air, communicate with the FSS to open and close your flight plan, give position reports and get weather updates and current conditions along your route.