From: New York City
Well, it took me a while to capture a battleship, but a couple of things I figured out:
1. Go for a Marauder first. They have fewer crew/marines than a Stonewall, which have fewer than a Gettysburg class.
2. Try to have 10-20 droids (not necessary, but it makes it easier)
3. Get the boarding shuttle upgrade- this increases your maximum crew load and guarantees that you will have the opportunity to board in any combat.
4. Find a battleship over a friendly planet. Go down to the planet, go to the bar, and get rid of all but about 5 crew. Load up on marines (? if there is need for officers). The key here is that as long as you are not flying to another planet, there does not seem to be any penalty for having less than the minimum crew (in combat for example).
5. Attack the selected battleship
It took me a couple of times but with a little luck, you can capture the ship. Once you make the jump to battleship, work your way up to a Stonewall and eventually a Gettysburg.