I’m just a hobbyist and these are my experiences…
While I don’t always take steam locomotive driving wheels apart, when I do I use the right tools from NorthWest Short Line (https://nwsl.com). I won’t go into a lot of detail on how to use these tools, so it is always prudent to read the NWSL documentation.
One example of when I will dismantle a driver is if a locomotive has a slight cyclical lope or lurch at very slow speed. In my experience squaring up the spur gear on the axle fixes or greatly improves this.
To start I photograph the driver pair that is dismounted from the engine frame. Taking photographs along the way is good insurance. If I forget how the wheel bearings go back on, I have the photo to refer to.
Held in a NWSL The Puller press fixture, I dismount the driving wheels from the axles using my NWSL Sensipress+. A pin that is smaller than the axle diameter is installed on the ram so that it will not interfere with the wheel axle bore.

With the wheel bearings removed, the axle and gear assembly is sandwiched between two steel NWSL The Aligner disks.

The top disk is firmly tapped with a hammer. To check for the squareness, remove one disk and hold the other with the axle/gear assembly up to a light. Slowly turn the axle watching for any light creeping in between the disk and gear.
To re-assemble: with a wheel bearing mounted on the axle correctly, the wheel is pressed onto the axle using the Sensipress+.

All dismounted driving wheels need to be accurately re-assembled: this is called quartering. That means the crank pin on one wheel needs to be precisely 90-degrees ahead of the other. On the prototype, quartering ensures that both crank pins are never absolutely horizontal to the piston centerline; in this orientation the engine could not start to move. Most North American roads used righthand lead, meaning the crank pin on the engineer’s side wheel is ahead of the opposing wheel in forward motion. The Pennsy used lefthand lead.
To accurately re-assemble the driving wheel pair, a NWSL Quarterer II is used. It has slots for both right and lefthand lead.

Most times driving wheels do not have the crank pins mounted, so temporary pins need to be installed. In the picture below, an MTH NYC L3a Mohawk driving pair is shown – note the brass pin installed, on each wheel. These are held with M1.4mm screws. The pins and screws are also from NWSL.

Then the other wheel bearing is installed correctly. This assembly is placed into one half of the Quarterer II as shown below – note that the axle sits in cutouts of the brass guides.

The other driver is placed roughly quartered onto the axle end and the other half of the Quarterer II is mounted. Ensuring that the crank pins are engaged in the correct slots for the lead, the Quarterer II is hand closed to the free wheel. It is good to check again that everything is where it should be. Note righthand lead below:

The Quarter II is mounted in the Sensipress+ and the free wheel is pressed slowly onto the axle, checking with an NMRA gauge. Assembly complete.

I ran into a situation with a brass model (Mizuno of Japan) where the thread for the crank pin hole was M1.6 fine pitch. I did not have screws for this and could not find any online. To get around it, I made up my own crank pins from styrene rod.

The smaller diameter is made from Evergreen 3/64” (.047”) diameter rod which is a nice close fit inside the crank pin threaded hole. The larger diameter body part is made from 1/8” (.125”) tube. .125” is a nice fit for the slots in the Quarterer II. I chose a section of tube that had the inside hole centered. The tube inside diameter measured to be under .080” so I used three strips of .015” x .040” longitudinally to make up the difference between the tube and the smaller rod. All this was assembled using Tamiya Extra Thin Cement (87038).
To avoid getting glue in the threaded crank pin holes, which I have no tap for, I held the pins in place with a retainer strip of styrene on the inside of the wheel. The strip had a hole drilled for the smaller crank pin rod. The retainer is lightly glued to the crank pin using Tamiya Extra Thin Cement.

This ad-hoc arrangement worked perfectly, and I was able to reassemble the driving wheel pair. As a bonus, I was able to lightly break off the retainers while saving the pins for future use.