To enter class C or D airspace you only need to establish two-way radio communications. You will also need two-way communications to enter class A or B airspace, along with some other requirements.

How to establish two-way communications

1. Tune the frequency of the facility you want to establish two-way communications with. If we were flying into Lancaster, pictured above, we would tune 120.9
2. State the name of the facility, your identifier, and your message or request. “Lancaster Tower, Cessna 12345, to land
3. Listen for your full callsign to be read back to you by the controller. “Cessna 12345, Lancaster Tower”

Once the controller reads back your callsign you have established two-way communications. At this time you may enter their airspace without further communication. However, the controller may say, “remain clear of the Lancaster Delta airspace”, in which case you are not clear to enter anymore.

Also, note that the exchange above is a bit contrived and the controller would ask you for your position, altitude, and if you have listened to the ATIS, so you should typically include these in your call to the facility.