For starters, look through the BOINCzilla bug database and try fixing a bug or two. Sign up for the boinc_dev email list to communicate with other BOINC developers. Also, read:

• Get and compile BOINC software
• BOINC coding style

• Core client: use the libcurl library or some other open-source HTTP library, replacing the HTTP_OP and PROXY classes. This would let the core client use HTTPS. (Carl C. is working on this).
• BOINC Manager: Change the Statistics tab to use a single graph with different colors for different projects.
• BOINC Manager: add progress bars for file transfers and in-progress results.
• BOINC Manager: add pie charts for disk usage
• Disk space management: prevent disk space usage from exceeding user preferences, and enforce resource shares, with file deletion according to project policy,
• Core client: use select() instead of polling for I/O (RPCs, file transfers, GUI RPCs).

Core client

• File structure
• FSM structure
• Data structures
• Main loop logic
• Client scheduling policies (new)
• Client scheduling policies (old)
• Debugging
• Host measurements
• Host identification
• Core client/application interaction (basic)
• Core client/application interaction (graphics)

Server programs

• The BOINC database
• Work distribution policy
• Backend state transitions
• The logic of backend programs
• Debugging server components

Protocols

• Protocol overview
• The scheduling server protocol
• Scheduling server timing and retry policies
• Data server protocol
• Persistent file transfers

Miscellaneous

• Python framework
• Preferences
• Trickle messages
• How to see what has changed between two versions of an executable.
• Account management systems
• Spec info for RPMs
• Statistics summaries