Being new to pen turning and wood working in general, I don't have a lot of the tools many of you may have. Also being cheap, I try not to buy anything unless I really need it. If I can get away with something else, I use it until I have to get the right tool.
As a pen press, I use my lathe. I take off the mandrel and the tail stock. I put wooden plugs that I made from scrap pen blanks into the holes. I push and lock the tail stock to the length of the parts I want to put together. Then turn the wheel of the tail stock to push together the pen.
It does get a bit tricky trying to hold the pen and turn the wheel at the same time, but once the parts go in a little, everything is held by friction. I'm sure a block of wood could be used to hold the pen parts while turning the wheel.
The big problem with this method is that sometimes, the pressure of the pen parts force the tail stock to slip. When the tail stock does not hold well, I just loosen it and re-lock it down. Usually it works after that.
One final note. Don't use a soft wood for the plugs. Since it will be put under a lot of pressure, the hardest wood you can use is best. Using Corian for the plugs may be good as well.
-CT