[Jeb]

To get boarding parties, you have to research Military Science up to level 2, and then at least one level of Ship Capture. Then you just have to move a ship with at least one boarding parties component next to an enemy ship and pick "capture ship" from the orders menu. This only works if the target ship's shields are down.

I'm not exactly sure how boarding works, but it looks like one level 1 boarding party will take out one crew quarters' worth of crew. So to board a base with two crew quarters and no security stations or anything, you need two boarding parties I. To tell you the truth, I haven't ever needed anything more advanced than that, so I don't know how it works with higher tech boarding parties.