I don't know what you mean when you say "Clock rates of computers are too high". Too high for what? They're high, yes, often as high as technology will allow (GHz), often as low as the application allows, for instance a 32kHz watch crystal, if only little processing power is required, or power has to be limited (power consumption is a direct function of clock frequency). Clock frequency is determined by the resonance frequency of a quartz crystal, and you can cut a crystal to about any frequency you want (see edit below). Sometimes processors run of a different type of oscillator, without a crystal, like RC, if the precision a crystal offers isn't required.
You don't use the 50Hz frequency to obtain a clock from, though it's not impossible to do so. It's much easier to use a crystal, like I explained above. In many cases, like for PCs, the 50Hz is only used for the power transport (transformers, overhead power lines). Once inside the PC it's converted to several DC voltages, and the 50Hz is no longer relevant. A PC can also run from a battery, and then there is no AC at all.
Like Cybergibbons says there's an upper limit for crystals' frequencies. He mentions 300MHz, Digikey's highest listed crystal frequency is 155MHz. Same Digikey lists crystal ocsillators up to 1.35GHz, but those are overtone oscillators. Other high frequency oscillators may use SAW (Surface Acoustic Wave) technology.
But even a 100MHz crystal can clock a 3.2GHz PC. This uses a PLL, or Phase Locked Loop. It has an internal variable frequency oscillator, and a frequency divider which divded by 32. The frequency this gets us is compared with the 100MHz from the crystal, and the difference (technically the phase difference) is used to adjust the internal oscillator to the required 3.2GHz. Since it has to cintinuously adjust, the 3.2GHz shows slight deviations, known as jitter. So a PLL clock is never as stable as its input signal, but for clocking a PC the deviations are negligible.
"Is the crystal oscillator fed by high frequency voltage"
When you switch a crystal oscillator on it's just an amplifier, you don't get the desired frequency yet. The only thing that's there is a low-level noise over a wide bandwidth. The oscillator will amplify that noise and pass it through the crystal, upon which it enters the oscillator again which amplifies it again and so on. Shouldn't that get you just very much noise? No, the crystal's properties are such that it will pass only a very small amount of the noise, around its resonance frequency. All the rest will be attenuated. So in the end it's only that resonance frequency which is left, and then we're oscillating.
You can compare it with a trampoline. Imagine a bunch of kids jumping on it randomly. The trampoline doesn't move much and the kids have to make a lot of effort to jump just 20cm up. But after some time they will start to synchronize and the trampoline will follow the jumping. The kids will jump higher and higher with less effort. The trampoline will oscillate at its resonance frequency (about 1Hz) and it will be hard to jump faster or slower. That's the frequencies that will be filtered out.
For most crystal this startup goes fast enough not to be a problem. But 32.768kHz watch crystals can only be driven with very low power, typically 1\$\mu\$W vs. 500\$\mu\$W for a 12MHz crystal. As a result a 32kHz crystal oscillator takes much more time to stabilize, often a few seconds.