Welcome to Inkscape development! There are so many different ways in which you can help. These are some starting points to help you find the best way you can contribute to Inkscape.
Core Inkscape Programming
If you are a coder/programmer and have some knowledge of C++ and / or Gtk development, grab the code and start hacking on whatever draws your attention. Send in a patch when you're happy with it and ready to share your efforts with others. We take contributions very seriously and follow the principle of "patch first, discuss later", so it is highly likely your efforts will appear in the development codebase swiftly. There are, of course, rules and standards that must be followed, but we try to keep them unsurprising and obvious.
- Getting Started – A guide on how to become an Inkscape developer, build it yourself and make it even more awesome.
- Coding Style – Inkscape's Style Guide. Please follow these guidelines when you write any Inkscape code.
- Inkscape's Repositories
If you're interested in becoming an Inkscape developer, of course you'll want to join the development mailing list, if you haven't already, and likely will wish to join the #inkscape-devel channel on IRC. And there is more info in the Developer Documentation section on (the bottom half of) the home page of the Inkscape wiki.
Dealing with bugs is a critically important job. This could involve submitting a bug to the bugtracker, writing a patch that fixes a bug or testing to see if the patches have fixed the issue. This helps keep the administrative side of inkscape's development in good working order and improves the effectiveness of developers as they have access to better and more accurate information.
See the Bug Management guide which will show you how to use the bug tracker to manage bug reports from users. It is highly recommended that you read it if you want to help in this area.
Inkscape is a large software project. Great documentation can help users get the most out of the software. Documentation can range from the wiki pages and website guides to wonderfully produced web videos that show users exactly how to use features and achieve results.
If you're interested in writing official documentation, please inquire on the documentation mailing list.
If you're not fluent with C++ (which is how the core Inkscape program is written) but you do know some Python and/or Perl, you might be able to write Inkscape extensions. You can find most of the info you should need on our page about writing extensions.