I'm guessing that the problems you ran into last time were in large part because you worked solo and came in under everyone's radar. If the project you're being asked to join has visibility, this shouldn't be an issue. However, you know have to worry about visibility within the team. People who pull surprises within teams can destabilize a project.

As for starting the project, my best advice is to listen carefully and gather information. What are the goals of the project? Who is the project sponsor? Who is the customer? How will the project benefit them? Who are the end users? What are their expectations?

When working on the project, manage commitments and expectations carefully. Don't bite off more than you can chew and swallow, and keep the team updated on what you're doing.