The basic overview is here.
To help render... You install the boinc client and join the project. The boinc client will handle downloading blender to your computer and render in the background. This is how you render (for yourself and everyone else).
You can still render images in your local blender application (i.e. you can still use your computer normally). The burp/boinc client will likely suspend burp rendering while you're rendering something locally.
When you submit a job, it gets accepted, and is sent out to all the clients for rendering. As each client finishes it's work, the rendered images are collected and stored on the burp server.
There is a java program called "CATS" that you can run to download your finished frames from the server. You can do this while rendering is still happening. As frames get finished you will download them (via CATS) in the background. Here is a faq about CATS. you can download the program here.
Hope this helps