I've probably replaced at least two dozen CRTs. I still take *extreme* caution when doing this. In fact, every time I do (just did two nights ago), I think to myself that I am being far too careful.
I always wear safety goggles. I don't wear gloves, but I always think I should.
The easiest thing to do (I haven't [yet]) is to break the vent stem off the back of the tube whilst unplugging whatever is plugged into the pins. Incidentally, if you need to dispose of a CRT for some reason, breaking that little tube is probably wise. It's probably the safest way to fill a tube with air. It will hiss for a while though..!
Long ago, I bought myself a high-voltage "probe". That is, a voltmeter for measuring 25,000V, and an analog one, not a high-impedance one. I use it for discharging CRTs. There is just no better way, in my experience, and I'm always glad I have it. In the distant past, I've used screwdrivers, homebrew discharging units, and I don't even remember what else. I've been shocked every which way, except when using the "probe." Similar to this:
http://www.ebay.com/itm/POMONA-Mo-3...327?pt=LH_DefaultDomain_0&hash=item51bbffc07f
Whatever method you use to discharge a tube, *always* redo it right before handling the 2nd anode button. CRTs, especially large ones, especially color ones, will redevelop a charge over time. So, you could discharge a tube, disconnect your discharger, and go back ten minutes later and get nailed.
Probably the scariest experience was trying to unstick a 27" 90 degree color tube from an old TV. It was *very* stuck, and the TV itself had no structural integrity; it relied on the CRT. So, nothing would hold still whilst I was trying to hammer that tube out.