It is the Trip Leaders responsibility to move people from the wait list onto the roster. Typically, the Trip Leader will vet the participants and if they do not personally know them, will vet them by the best available information including asking for a resume, looking at event histories and talking to other Trip Leaders. You should not have a first-come, first-serve expectation considering that a participant without the required fitness, skill and equipment will prevent the success of the group achieving their goal. Vetting participants is widely considered the most unpleasant bit of leading a trip. A Trip Leader is taking a gamble taking anyone they have never met into the mountains. If you are new to the club, make it easy on the Trip Leaders and meet them at a training night, slide show, social or a climbing/ski review (these events are usually first-come, first-serve). If a Trip Leader can put a face to a name, you have a much better chance of getting onto a trip. It is also a good idea for participants to vet Trip Leaders as you will be trusting them with your safety.
If you sign-up for a winter trip, make sure you take your AST level 1. If you sign-up for a climbing trip, try and climb with the Trip Leader at a gym or rock rage night. Finally, be reliable. A no show on your record will drop you to the end of the selection list in most cases.