Yes it needs to be square and all, but in my experience, I have found that the gun is designed well to sit naturally in the correct positions for pressing.
First is the barrel pin. If you get the rear sight out of the way, the side of the trunion lays flat on the press plates. I often support it without a hole underneath and use a stubby punch to get the pin moving, then put a plate under with a hole and use a longer punch for the rest of the way.
Then the barrel. The trunion has enough "edge" to set up on standard press plates (which usually have square and round indentations) and support it all the way around. Be sure to use a soft something between a steel push rod and the breechface so you don't scratch it... nickels work well.
Pulling sight blocks and such is similar.
Putting the barrel back in is pretty simple. I have seen people support it directly on the bullet guide (through the magwell), but I don't do that as I think that would put too much shear force on the bullet guide rivet. I use the top part of the trunion and hang it on the press plate. It's a little precarious, and I use some brute force, gloves, and of course eye protection.
The best thing to do is take a beater kit for your learning curve, and experiment...pull the barrel, put it back in, etc. If you scratch it, you don't care, it's a beater...
Then you can get good at it and get questions answered from your experience, feel confident, and go on to the next projects...
Good luck..