The main radio frequency of VOR transmission - your example is 113.4 MHz - does not change. What the conventional VOR does is transmit a tone on that radio channel, and then modulate the tone. This tone is called a subcarrier, but it's a carrier in the sense that it is carrying information, not in the "radio" sense.
That transmitted tone is frequency modulated with a sine wave, and your VOR receiver can demodulate it and gets back the corresponding sine wave. The tone is sent at 9960 Hertz modulated +/- 480 Hertz, and the sine wave that it carries is at about 30 Hertz. This sine wave is the reference signal.
By the way, since 9960 Hertz is in the audible frequency band (or at least, it was when I was younger) if you tune in a VOR with a ham radio type receiver, you can listen to it going "weeweewee" in a fairly unpleasant chirpy way. Fortunately the VOR receiver in your aircraft has audio filters that remove this. That filter doesn't block lower audio frequencies, and that's how you can get the ident, and in some case audio (such as ATIS weather) transmitted on the same VOR at the same time.
Back to the VOR - The second half of the VOR solution is that the whole signal - meaning the transmitted 113.4 MHz signal (which also contains the reference and the audio stuff) varies in amplitude. In the classic VOR design that's because the VOR antenna itself whirls round with an electric motor (although the reality doesn't involve a huge antenna going round, and actually involves some transformations that are beyond this tutorial, but just imagine an antenna whizzing round and you get the idea). The antenna whirls around at the same 30 Hertz rate as the reference signal. When it is pointing straight at you, the signal is loudest, when it is pointing away, it is quietest. It is therefore amplitude modulated, and we can demodulate that as well.
Since the reference sine wave does NOT come from the modulation of the 113.4 MHz signal, but instead comes from the modulation of the high pitched audio tone we transmitted, it is not affected by this whirling of antennas, and it sounds exactly the same wherever you are. But, the relative peak of the amplitude DOES depend on where you are (because the antenna is going round). By comparing the peak of the reference sine wave with the peak of the overall received signal, we can work out the phase difference between the two. If we measure that in degrees of phase, it will be a number between zero and 359 degrees. Which can very conveniently be correlated with the radial from the VOR transmitter.
