To participate in a hackathon with MongoDB, you need to set up your environment by connecting to your MongoDB database instance and downloading the MongoDB Shell and Compass. You can use MongoDB Atlas, a cloud-based database as a service, to simplify the process of setting up your database. Once you have your database set up, you can focus on building your application using MongoDB Stitch, which provides an automated system for deploying and managing databases and backend services. With MongoDB Stitch, you can create a rule for your database and collection, import mock data, and expose your data in an application via the Stitch SDK. The entire process should take around 30 minutes to complete.