To board a ship, you need to either be in control of it, or be on the crewlist. If either of those applies, stand in the same square and there should be an "Enter" button on your position -> travel screen (same as for entering a facility). Then select the ship. If no ship shows up, you're not allowed to enter it.
NPCs should be showing up blue on your scanner when you're looking at people, and will come up with a set dialogue when you try to hail them.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."