Write down the information that the problem gives you. For most classic problems requiring you to calculate RF frequency, the problem will tell you the inductance and the capacitance of the resonator in question.
Draw out a circuit model of a resonator, and make sure that you understand how they work. To tune a radio, you use a simple circuit called a resonator that consists of an inductor and a capacitor that is configured to be more sensitive to a particular frequency. When you adjust the dials on a radio, you usually change either the inductance or the capacitance of the circuit in order to change the RF frequency of to circuit and switch to a different radio station.
Convert the capacitance and inductance to the units that you need them in, which are farads for capacitance and henries for inductance. Because farads and henries are such large units, you will rarely see them listed in a problem; the problem most likely lists capacitances in the microfarad or millifarad range while giving you the inductance in nanohenries or microhenries. Make sure that you convert the units properly, or your calculations will be off by several orders of magnitude.
Multiply the converted value of the inductance by the converted value of the capacitance. For a circuit with a capacitance of 0.0001 farads and 0.05 henries, your total value would be 0.000005.
Take the square root of the number that you got in the previous step. For the previous inductance-capacitance value, the square root is 0.0022.
Multiply the number that you got in the previous step by the constant pi, which is roughly equal to 3.14. If you have a scientific calculator, it can probably multiply your previous number by the exact value of pi, but the approximation should work pretty well for most purposes.
Double the number that you got in Step 6.
Divide 1 by the number that you got in Step 7 to find the final RF frequency of your circuit.