There is a long list of tools that are nice to have for pen turning, but most of the tools required are simple hand tools.
A lathe is needed, but people have used a drill press and turned pens vertically.
A pen mill is used to true up the ends of a blank. Chuck the pen mill in a hand drill.
A miter box and hand saw are sufficient to cut pen blanks into upper and lower halves.
Superglue (CA), Epoxy, or polyurethane glue will glue the brass tubes into the pen.
Sandpaper for surface preparation.
A press to press the fittings into a pen. A vise of some sort with soft flat jaws or a Quick squeeze vise.