The Rudder shaft.. the hull should be drilled to accept the rudder TUBE dia and glued in place, you can do this with just glue around the tube inside the hull or make a tube block which gives the tube more security and stability long term...( shaft block are my chosen method)
theres no reason why you cant install the tube after painting however you run the risk of chipping paint, idealy the tube should be fitted before painting to avoid this along with the fact it gets a lick of paint too.
the rudder and its shaft can usualy slide up the tube in the hull and is secured by a nut at the top ( if its threaded) and a tillar arm whih screws to the shaft to lock it, some people opt to file a flat where the tiller arm grub screw hits the shaft to give a more secure connection. ( more so if there is no thread on the shaft for a lock nut to stop the shaft dropping out...)
if you dont have a theaded shaft.... my chosen method is to cut one on.. loosing a rudder mid sail is poor form!
this applys to ' most boats' so simple operation of a normal rudder....
That said many boats have rudder skegs, this means you have little choice but to make the skeg, thats the end of the rudder inserts into removable to allow you to put the rudder in and out.
i have seen many people put the rudder in and glue on the skeg and paint in one go.. frankly i find that amature'ish' as there is no way to remove the rudder after its installed....
As for attaching the rudder to the shaft
that depends what material its made of..
plastic/wood rudder to metal = epoxy ( regardless which metal) extra then add two pins through the rudder and shaft to give added security if the shaft is ' slotted ' 9 basically any slotted shaft for rudders you would use two pins + the attchement methods to secure)
brass rudder to stainless shaft, = silver solder
brass rudder to brass shaft = silver solder, but soft can work well.
white metal to white metal .... = remake that entier junk from brass!
to make the skeg removable you need to make up the skeg with the intension of it being screwed to the hull, or the remainer of the skeg thats still attached to the hull.
On a model the skeg generally is more for accuracy of the model its fuction is limited as its a fragile part anyway in any model size...
a removable skeg is the best way to install not only the shaft but the rudder as your able to remove it consistanlty for maintence/greasing.
my chosen method for skegs removal is to make skeg of brass, counter sink the holes for the screws, as this part becomes on solid part thats very durable, but takes paint poorly... ( i enamel it later) other option if its GRP works the same as brass, but wooden skegs would require a little reinorcement which i suggest using some glass cloth & epoxy to add strength to it where the screw holes are countersunk i would also add some of the brass bushing from servo mountings to help the screw joint less 'weak' . if the skeg is of ''white metal/puter'.. bin that shit and make if of brass! white metal skegs are junk there is no other way to say it...
see attached photo of my springer tug with a detachable wooden skeg...