CRT monitors can hold up to ~15-25,000 volts, some going up to ~50,000 volts (usually reserved for TVs or monsters like the GDM-FW900)! While this is the generally accepted rule, you should not assume this is going to be the case every time. Treat the monitor as if it is holding the higher voltage average between 15 and 25k at all times, especially as some “professional” CRTs like the FW900 (and FW900-derived rebadge monitors) are likely to exceed 15k volts due to the CRT size and go into the 20-25k range out of necessity for the giant 24" 16:10 CRT due to the sub-2K resolution tube.
IMPORTANT: Most modern CRTs (90s-final production) have a bleeder resistor, but this is often burned out and cannot be relied upon to work! You still need to discharge the tube to be safe -- DO NOT TAKE ANY CHANCES! Anything from the 80s is dicey, and 70s or older doesn’t (or it died decades ago).
Unless you know what you’re doing, you are usually better off leaving the repair to someone who knows how to do it safely or replace it. These monitors hold enough charge to kill you if you screw up.
That said if you still insist on trying and we can’t stop you, you need to take precautions. The best advice I can give you that isn’t covered is to ALWAYS keep one hand behind your back - this will prevent a circuit from forming if the charge chooses your hand as the path of least resistance. DO NOT have both hands out at the same time - THIS CAN CREATE A HEART-STOPPING CIRCUIT WHICH CAN KILL YOU. In addition to that, if you wear any jewelry, it is imperative you take this off. This will become a hazard if you slip up as it is an excellent conductor. Remember: electricity takes the path of least resistance.
If you do not know where to get a real discharge tool (or have one) since they’re hard to come by these days, it’s okay to use a rubber-handled screwdriver with an alligator clip lead, but do not want to use the ones from Radio Shack or Fry's; they will burn up. Use car jumper wires if that’s all you have - it’s overkill, but when dealing with 15-25,000 volts you’re better off going overboard to be sure it will not bite YOU and potentially kill you.
Before removing the anode from the tube, ALWAYS TOUCH THE LEADS WITH A GROUNDED SCREWDRIVER FIRST! This ensures the monitor has no charge left. Failure to do this CAN KILL YOU.