I would argue whether two-person project requires extensive project management knowledge. Actually, it is more about some basic planning and organization and a lot of collaboration. Fortunately the latter mainly between two people.
Leaving aside a crucial part of collaboration with your peer, the rest of project management effort should likely boil down to a few areas:
- Scope management
- Task organization
- Product management/product ownership
- Communication with clients and/or users
Depending on your situation one or more may be less important then the others. You can see a bit more explanation of each these areas in this post and in this PMSE question. Context of these sources focuses on one-man project, yet most of the time, your situation should be very similar.
I would add to these sources that in terms of task organization techniques and tools known under the name of Getting Things Done (GTD) might be useful and at the same time they require little initial investment.
In terms of collaboration, with just two people, I'd just try to find it out experimentally what works for you two best. Be it pair programming all the time or splitting the project into two separate parts and working on them independently or whatever in the middle--as long as you talk one with the other you should soon find out which approach you like and which makes you effective.
Knowing which areas you want to focus at it is a good idea to address the knowledge gap. I would probably recommend Peopleware and/or Making Things Happen. In both cases please do remember about your specific context, which is a very small team, as much information covered in books on project management typically address more complex environments.
Then, the final advice: experiment with the way you work. Such a setup is a great sandbox to learn as you can adjust your methods, practices and tools rather easily. It's enough to convince the other person that it's a good idea to try this or that.