The tools are purpose built. There is really no specific order or “right” way to do it, but there are a lot of wrong ways. Coming from empty brass at the range, the brass needs to go through a few steps before it can be shot again. Some folks reorganize this list a bit but I do it the most logical way. I will hit the basics...
1 clean the brass. You have a vibratory tumbler for this process. Run the brass for a couple hours and let the corncob or walnut media break down the crud for you. Do this first so that said crud never gets into your reloading tools.
2 deprime. Gotta get the old primer out. There’s a stem that is in one of the dies that does this. It has a long narrow rod on it that goes through the flash hole and shoves the old primer out. It’s usually on the sizing die which simplifies things.
3 sizing the case. When fired the case swells a bit and has to be put back to original size. The resizing die does this. This often also bells the case, but that may be a separate step in some die sets. But it’s what it sounds like, you want a slight bell shape on the top of the case so that when you put a bullet in that it doesn’t get cut or crush the brass.
4 prime. Need a new primer to set things off when you go to shoot. Priming on the press is common, but so are separate tools. If you see something that looks like it takes a shell holder but has a tray on the side and is a kinda wierd shaped spring loaded grip thingamabob that’s probably it. I see at least 1 press mounted primer arm so I assume that is what your dad was doing.
5. Charge. Gunpowder is not EXPLOSIVE but it is a a very fast burning propellant. Different powders burn differently and have to be measured very precisely and then metered out just as precisely to make sure it’s repeated properly. This is the most important step because doing it wrong either way presents dangerous conditions. Too light of a charge can let a bullet stick in the barrel (squib) and the next bullet being obstructed can blow up a gun. Too heavy of a charge can blow the gun up as well. Gotta know what powder your using and follow the books.
6 Bullet. The bullet has to be shoved down into the case. Again, this is one of those consistency things. Often times this step also crimps which is the point of removing that bell you put on the case earlier.
7, crimp. Crimping can actually bite down into the bullet a bit to help hold it in place so that it doesn’t get pulled out by recoil or shoved into the chamber during loading in a semiauto, but again, the purpose is to remove the bell and hold the bullet in place.
Most dies are cartridge specific. Every now and then you will find something that works in multiple ways, or on multiple things. Universal depriming dies are one example, which essentially it’s just using using the depriming stem without any kind of resizing operation.