I've been working for three years in my current company and at the same time I took part in over 10 different projects for various clients. Changing projects this often taught me how to onboard quickly to new project and contribute as soon as possible.
This should be the person who knows the most about the project, especially from the business side.
- ask her/him about project background - what we are developing and why
- ask about the last milestone they achieved
- ask about what they currently work on and what will you do
- what is the team currently struggling with - maybe you can offer your help here
Project teams may have various sizes. It could be 2 developers working together or even team of 25+ people. In small teams it will be very easy to work closely together. In bigger ones, usually there will be a person or two who will coordinate the work of the team.
When you meet your new team mates get to know them from personal level, but also ask what are their responsibilities in the project. It will be easier to find a person who can help you later.
This will be the person you can ask questions directly about the projects. Usually it will be the team leader or some other experienced person in the project. Ask them to show you how they work, what is the development flow here and how is the application working.
It should be your first technical task. Depending on the project it may be as trivial as running 1-2 commands or require even a few days to install and configure all dependencies. While setting up your local development look for things there are missing or outdated in project documentation and offer to fix them. The new person who will join the project will thank you for sure.
You are just beginning your work in this project. Do not expect from yourself to deliver something meaningful in the first weeks. It will take time to get to know all details of how your application works. Your team mates are months, if not years, ahead of you when it comes to project knowledge and they are able to quickly find a place in the code where this small change is needed, while you might spend several hours on the same thing. Do not worry about it, you will get there.
I know you would want to put you knowledge into practice and deliver great feature in your first week, but it would likely take 2-3 more time than initial estimates of your teammates and that's ok. I would suggest to look for small tasks at first - changing a translation, improving the design, adding some field to form. You will pick up knowledge from different places of the application and you will be able to use it soon.
While working in the project look for ways to improve the project. It could be contribution to documentation or refactoring some parts of application everyone wanted but nobody did it. Looking at project with fresh eyes you may discover some improvements that were obvious, but went unnoticed by your team mates. Maybe you can introduce some interesting practice or tool you used in previous project / job?
Working in a new place and new people is always stressful, especially the first days. Remember to focus on learning as much as possible and do now worry strictly about delivering features. After few weeks or months you will start feeling comfortable and work in your standard level and pace.