First thing to do which sounds stupid is unplug the machine (obvious I know but it's best to double check) the power supply you will be able to pick up and take out without any problem, as far as the monitor goes rule of thumb is handle it by the frame, do not touch the pcb or tube and definetly don't touch the anode cap or big red wire. If handled with care and respect you will not get a shock. Certainly if you are not sure or feel like removing it yourself then get someone to do it.

Regards.
EDIT: Just as a follow up Pinx over at Jamma+ done a good write up on monitor's
1. Always Disconnect the cab from the mains.(that means unplug it, not just switch it off !)
2. Never go into the back of a monitor with both arms (if you were to get a shock, it would cross your heart !!).
3. Always discharge a monitor first, before working on it (unless its just screen adjustments).
4. Use the correct tools to discharge a monitor and carefully read up on the proceedure to do it. (tubes can rebuild charge after you have discharged them).
5. Be very, very carefull when removing a monitor or moving it about, as the CRT (Cathode Ray Tube) is a bit like a bomb, if you mishandle it or drop it, it will implode first before it chucks fragments of razor sharp glass upto 30 feet.
6. Be aware that large capacitors hold lots of charge and if you accidentally short between the pins with your wedding ring or that screwdriver you were having a prod with, its gonna go bang...
7. If in doubt, DO NOT TOUCH is a brilliant motto, use it.
8. Never be affraid to ask for advise or help. It never pays to guess or assume.
9. Learn how to solder properly, to a competent level, no use fitting new parts, if your soldering has caused a short to something else.
9. Always use the correct parts with the correct values, dont think "well it looks the same it'll be ok". And make sure you fit the parts correctly, most components have a polarity !
10. Finally, when you fix that Hantarex 9000 with frame collapse all by yourself, and your stood there blasting away at Nemesis thinking "this is great, i fixed this"
Be thankfull that you followed all of the above and are not laid in a Hospital somewhere.....
Pinx
As I have said already if you don't want to do it yourself get someone who knows what they are doing, safety first.
