How? Very, very carefully.
Typically one end of the CRT is at -2450V, and the other end of the CRT is at +15000V, the focus is at -1400V, and other terminals are at a mere 120V. There are capacitors at those voltages, and they will store enough charge to bite. Make sure you understand the cause and consequences of dielectric absorbtion, a.k.a. soakage, before you fiddle with those circuits. If you are a beginner, seriously consider not fiddling with those circuits.
I would guess that the deoxit (and there are many different types of deoxit) deposit has been sufficient to allow those voltages to short out parts of the circuit. If that is the case, then your first task is to thoroughtly remove any deposits, probably using IPA.
If the brightness is full-on then there will be a problem with the grid bias. I had that on a scope, and it turned out to be a disconnected grid inside the CRT ( if interested, see blog in my .sig). If your scope was working before, then I doubt that's the problem. Most likely the HV diodes in the grid circuit have been destroyed, but there may also be HV capacitor damage. If you replace the diodes, make sure you get the voltage, current and speed correct, and check whether you need special solder containing a small proportion of silver.