You will easily see when a NPC wants to join you as his ouftit will change to your actual crew's ouftit when he's willing to join you. The first one being they betray your trust and attack you again, Or they thank you and ask to join your crew as an outlaw.

Showing mercy to them can have either of two results. After you take out most of their health, they will 'surrender' and ask you to lower your weapons. The third way only requires that you accept a 'NPC fight mission' in wich you have to fight a warrior.

The second option is to buy a colony deed at the outpost's furniture shop, build or find a suitable 'house' (a closed room with a least one door and a light) and place the colony deed inside, a NPC will spawn (note that depending on the furniture, the type of NPC will change) you can then wait for his quests and complete them, and hope that he asks to join the crew. There are currently Three ways to get NPCs to join you, the first and easier one is to find a NPC giving quests anywhere, complete their quest(s), and with some luck, the NPC will ask to join the crew of your ship.

Starbound how to get a crew