CRT Repair Cautions
When working on a CRT attention should be paid to the charged state of the display tube. The dangers of being shocked are frequently characterized as being lethal, which is a gross exaggeration. You can be shocked (and the author writing this has) by a CRT and suffer no ill effects other than surprise and embarrassment. The severity will depend on the characteristics of the tube though.
CRT Charge
CRT stands for "Cathode Ray Tube", where the cathode generates an electron beam that is moved across the phosphor coated tube to produce light. This is somewhat unintuitive with the concept of "conventional current", the idea that current flows from a positive charge to a negative one which is the way most electronics is taught and presented. The reality is that electrons actually flow from a negative charge to a positive one. This fact has actually been used for multiple types of display technologies like Vacuum Florescent Displays and Nixie tubes which don't use Black-body radiation to create light unlike an incandescent bulb. The electrons hit a phosphor layer in VFDs and flow through a gas in the case of nixies that they interact with causing the glow. But VFDs and Nixies operate at dozens or a few hundred volts instead of multiple thousands like CRTs. CRTs need the electron flow to be fast and precise, so they use a vacuum like VFDs but increase the voltage difference significantly.
CRTs also have two conductive coatings applied to the on the inside and outside. The inside carries the anode voltage and the outside is connected to ground. This was done to use the CRT itself as a capacitor to smooth power fluctuations in the anode voltage. The glass of the tube acts as the dialectic barrier to form the separation. The CRTs capacitance will depend on its size which increases the amount of parallel surface area, but the total capacitance will be considerably less than 1uF. This means the total power stored in the CRT is not significant. A 1uF capacitor charged to 20,000V would only hold ~0.05Whr of energy.
CRT Shock Hazard
As explained above, CRTs store a small amount power as a capacitor themselves. The shock hazard comes from the fact the charge voltage can be higher than the dialectic breakdown voltage of air, which allows the charge to form a spark gap. This spark gap must have a path from the anode of the CRT, to the outside conductor of the tube to connect the two sides of the capacitor. Since the outside conductor is typically grounded, anywhere on the chassis of the device can act as the cathode to the CRTs anode. The only way to access the anode is under the anode cap though, the inner coating is not externally exposed. The anode cap is connected to the flyback transformer, but due to the isolated nature of a transformer you cannot come in contact with the anode through its connections to the PCB. So if you do not need to remove the anode cap, you are unlikely to come in contact with both sides of the CRT charge and be shocked. The only time it is likely to happen is when you need to remove the anode cap, which should only be needed when removing the PCB the flyback transformer is mounted to.
Discharging a CRT
Since the CRT itself functions as a capacitor, the way to discharge it is to connect the anode and cathode to allow for the voltage potential to equalize between them. The CRT does not need to be connected to earth ground to achieve this. To do this you need to connect the clips of the anode cap to ground on the chassis. The most difficult part of the process is is getting a conductor underneath the anode cap on the CRT which may be "stuck" to it if it was applied with a grease. Using a non-conductive tool to first life the silicone portion of the anode cap can be helpful. A simple way of then connecting the anode to ground is to use a wire with clips to connect the chassis to a flat bladed screw driver and then tap the clips of the anode cap with the screwdriver. You will most likely hear and potentially see a spark when the discharge happens.
Some CRTs may have a "bleeder" resistor installed which connects the CRTs anode and cathode. This will be an extremely high value resistor that won't allow much current to pass through, but once a CRT has been turned off will slowly dissipate the charge. If you attempt to manually discharge and do not hear or see a spark this may be why.