Your first post
This will no-doubt be the first time your character comes aboard the Blue Dwarf and meets other characters. Try and make your entrance as memorable as possible, so that people will "get" your character and include them in their stories. This doesn't mean they come in singing and dancing and making a spectacle of themselves (unless of course this is typical of your character!), but try to do something that typically defines your character.
If they are clumsy, write them making a tit of themselves in front of everyone and being embarrassed. If they are incredibly kind, introduce them being nice to someone. If they are incredibly arrogant, show them being incredibly arrogant. You can develop the characters much further than just these simple qualities, but it's somewhere to start rather than "Bob meets Frank and says hello. Frank waves neutrally at him."
How will your character come aboard?
You have an infinite choices for how your character meets up with everyone else. You can either create a long and complicated backstory where you are being chased by a gang of alien mafia, and have to seek refuge on the Blue Dwarf, or you could meet up with a team on an away mission and earn their trust, or you could simply say you've been part of the crew for some time but haven't been mentioned yet.
Many people go for the last choice, which is the easiest, and there is no shame in doing so. It saves writing a complicated back story, and also gives your character an existing familiarity with the Blue Dwarf.
Stasis
If you want to start afresh but without the hassle of a back story, you could say that you have been in stasis for the majority of this mission as a “backup crewmember” and you have been brought out of stasis now. You will be able to mention that your character doesn't properly know their way around yet, and start to meet new people.
See things from an alien's perspective
If you are playing an alien or gelf and have just come aboard, you might want to mention how different the Blue Dwarf is to your home planet. The things that we take for granted might be strange and unusual to an alien, so it could be worth pointing little things out.