How does VCO in PLL in computer processor work?
Is that [VCO] a crystal rather than RC circuit?  


VCOs don't use crystals†, but VCOs don't necessarily use a RC circuit for timing either. Voltage controlled oscillators are a broad class of different designs.
Crystal oscillators are frequently used to generate the reference frequency for a phase locked loop (PLL), but phase locked loops are not VCOs. VCOs are a building block of PLLs.  

†Crystal oscillators whose frequency can be very slightly tuned (only a tiny fraction of a percent) with a control voltage do exist, but they are probably not what you meant.


  Is it [VCO] tuned by varicap?  


That's like asking "are trucks powered by diesel". Many (especially harmonic oscillator-based) VCOs are, many (especially relaxation oscillator -based) aren't.  


  Does it [VCO] contain reference voltage and comparator?  


Relaxation oscillator -based designs usually do in some form or another, but other VCOs use a different mechanism.


  Is frequency of the internal crystal the maximum possible output frequency?  


VCOs don't generally have crystals, they are just oscillators whose oscillator frequency is roughly but monotonically proportional to the control voltage. You might be thinking of phase locked loops (PLL), which often (but not always) use a crystal oscillator as a reference oscillator. A PLL is a circuit which produces an integer multiple of a reference frequency by automatically tuning a VCO to keep it in sync with the reference.
The output of a PLL is not limited to the reference frequency (which is often generated by a crystal oscillator), it can go many times higher than that. That's a big part of the appeal of PLLs.


  Does VCO work on clock signal or continuously?  


Continously. They may output a clock signal, they don't need one themselves.


  What is the physical principle behind changing the frequency? Can I see graphs explaining how it works?  


You increase the control voltage, the frequency increases. I don't understand why you'd want a graph to understand that. The physical principle varies, but in general there are two types:  


Harmonic oscillators use a wideband amplifier feeding back into itself. A specific frequency can be generated by adding a band-pass filter into the feedback path, so that only oscillations at a single, desired frequency can sustain themselves. To change the output frequency, the filter is modified so that the passband is changed, achievable with e.g. a varicap. 
Relaxation oscillators repeatedly charge and discharge an energy storage element like a capacitor or inductor, with the charge and discharge time determining the output frequency. The frequency can be varied either by changing the capacitor/inductor charge rate, or the thresholds at which the circuit switches from charging to discharging and vice versa. This type is what you usually find as part of the clock generation circuitry of digital electronics like microprocessors.