Hi Luc,
Here's a basic step-by-step. We just got done figuring this out.
1. Create a D2L user account with appropriate permissions. This is not a "special" account and has no special settings, checkboxes, etc. It's just a user with rights to see (and possibly alter) the information it needs to operate on.
3. After logging in, the API test tool will have string values in "User ID" and "User Key" boxes. Copy these and store them somewhere secure, but also where your application code can access them.
4. When creating your user context, feed the user ID and user key values you copied into the D2L context object. This is done differently with each language's API. If you run into trouble here, I'd suggest either searching the forum for how to do this, or posting a question specific to your API language.
5. You can now use the resulting context object to send Valence requests just as if your user had authenticated manually.
I'm writing off the top of my head, so do post up if you run into snags. The information on how to do this exists, but it's all over the place and hard to piece together, so I hope this at least gets you going in the right direction.
Good luck!