The most reliable way of obtaining a large crew is to defeat hostile ships by killing all the crew (i.e. leaving the hull intact) whenever possible. This gives you lots of chances to pick up additional crew members, and also yields more scrap, weapons, and ammo, enabling you to purchase more crew when you come across them for hire at a station.
The most effective way of doing this is to teleport your crew onto hostile ships and engage the enemy in hand-to-hand combat, so invest in a teleporter at the earliest opportunity.
There are also a few things that give you access to blue options in certain situations, occasionally increasing your chances of obtaining more crew:
- Sensors 2
- Teleporter 2
- Med bay 2
- Have a slug crew member
Those are the ones I know of - there might be others.