high frequency transformer basics
High freguency isn't a well defined term. Most of us surely think that HF transformers are complex to design, analyze and make, because several non-idealities grow substantially as the frequency increases. For example many iron cores, which are excellent for 50Hz transformers, become awfully lossy when the frequency is only few kilohertz. 

Some common non-idealities (harmful or useful depending on the application):


losses in the core material
limited permeability of low loss core materials
saturation in core materials
currents through the stray capacitances of the windings (=> parasitic LC resonance circuits)
voltage loss due the leakage inductance of the windings
increased resistance of the windings due the skin effect
losses in the insulation materials
tendency of catch and spread unwanted interference 


The working principle of HF transformer is the same as 50Hz transformers, only the non-idealities should be taken into the account.

The thinking principles (see NOTE1) "for what to use a transformer" have more variations in radio or switchmode power supply circuit design than at 50Hz. High frequency transformers are used often also


for impedance matching
as resonant filtering circuit at the same time as changing the voltage or matching the impedance
as inductive energy storages at the same time as changing the voltage (flyback power supply)
for directional signal coupling (the same has been done at audio frequencies in ordinary landline phones to keep talkers own voice and ambient noise out of his own ear)


Many of the radio applications of transformers can be alternatively be realized with well calculated transmission line circuits. Thus some widely used transmission line constructions are called transformers. Most common of them is obviously the quarter wavelength transformer which changes the impedance.

Transformers do not change the frequency except the cases when the nonlinearity of the core material cause distortion, which generate new spectral components.

NOTE1: that's only thinking, the physical function of the transformers stay unchanged