Yes, this is something you can breadboard quite easily. (High frequencies might be a problem on a breadboard, however.)
There are a few ways to go about it but most circuits use, in addition to the crystal, just a couple of inverters, a few resistors and a few capacitors. Do a Google image search on "crystal oscillator circuit" to see some examples.
They make ICs specifically made for this too.
For example. Notice (page 7) that all that IC really does is package-up the inverters. You still need to provide the capacitors, resistors and crystal.
Finally, in case you aren't aware, they package the whole crystal and other necessary components up into a single package an call it a crystal oscillator.