Taken from:
http://www.cs.uu.nl/wais/html/na-dir/apple2/faq/part16.html
What Safety precautions should I take when working on my monitor?
Basically: unplug the monitor and let sit for a day, wear goggles, work on a non-conductive table surface, do not stress CRT neck.
Unplugging the monitor and letting it sit for a few hours reduces the danger of shock from stored charges; it does not eliminate it. The usual warning for this kind of work is AVOID touching two different circuit points at the same time. Like, don't touch the metal chassis and the conductive surface of the CRT at the same time.
WEAR protective GOGGLES. If you should, somehow, bump or stress the CRT neck-- as in jumping when you get shocked-- it may break. The result may be a peaceful THOOP! or the CRT may implode in a spray of glass. (Avoid using the CRT's neck to support the monitor in any position.)
Work on a wooden or plastic-topped table with plenty of space. Try to position yourself, tools, and the monitor so that when you get 'stung', the chances of breaking something are reduced.
As much as possible, avoid using heavy tools of any kind. An inadvertant tap from a mini-screwdriver is much less likely to crack the CRT than a bonk from a full-sized screwdriver or pair of pliers.
Rubber gloves are probably a good idea so long as they do not get in the way. Of course, pointy connections and components can puncture gloves.
It's a good idea to clip a wire to the chassis and touch the other end to the conductive surface of the CRT a few times before doing any work in order to drain off any charge there.
Note: Several places in a monitor or TV carry high enough voltages to deliver an uncomfortable shock. Draining the charge from one point does not guarantee that other points have been discharged.
How do I discharge the High Voltage?
The HV charge (20,000+ volts) might not be much reduced by just waiting a few hours (or days), especially if you are in a low humidity location and the tube, etc., are of good quality. You can, probably, _reduce_ the shock hazard by discharging the High Voltage at the anode. You can not, really, expect to eliminate the shock hazard. (See WARNING below.)
1. There is a long wire (called the anode) that goes from the high
voltage power supply to the top of the tube where it is snapped
into a hole. You can't see the hole because there is a rubber
shield built onto the wire. The end of the wire goes to a metal
clip which, without the rubber shield, looks somewhat as below.
One squeezes the clip so the end slips into the hole in the tube.
--- ---
= \... / ===== back of CRT
==\ / <-- metal clip (This is what your grounded
.==| screwdriver needs to touch.)
==[|]
==[|] insulated Anode lead going to HV module
==[|]
Needless to say, UNPLUG the monitor before beginning. Simply
turning it off isn't good enough.
2. Get a clip lead and clip one end to a long slender screwdriver
3. Clip the other end to the metal chassis of the TV (i.e the
metal frame parts)
4. Carefully! slip the screwdriver tip under the rubber flap on the
top of the tube until it touches the internal wire that both
holds the anode wire in place and conducts electricity.
Step 4 may result in a somewhat loud "SNAP" as the tube is discharged. Be prepared so you don't jump and break something.
WARNING: After "discharging", do _not_ assume that no High Voltage is present. Almost certainly, some High Voltage remains or may reappear over time.
Another how-to/warning link
"NEVER OPEN THE CASE OF ANY VIDEO TUBE DEVICE, UNLESS YOU REALLY KNOW WHAT YOU ARE DOING
YOU MUST KNOW EXACTLY WHAT YOU ARE DOING TO HANDLE A CRT SAFELY."
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In other words, messing around inside a monitor is not something to be undertaken lightly.