Moreover, contributing to open source is easy for me, but I'm already an open source contributor. For new contributors, the process can be really daunting, for a variety of reasons. I'm going to go through a list of things that projects can do to encourage contributions, roughly in order of increasing difficulty.
It's really surprising how few open-source projects even get this far. Every project needs to have a page somewhere that says something along the lines of, "If you want to contribute, we could use a hand with X, Y, and Z. Contact so-and-so for details." If you don't say something like this, most people - especially those that aren't familiar with open source - will just assume that you don't really want outside contributions.
Keep some easy bugs around for new contributors
This is pretty easy for any project that has a reasonable volume of bug reports coming in. Invariably, some of them will be for really easy stuff - spelling fixes in documentation, or other really trivial fixes. Instead of just fixing these, give them a special tag or something on your bug tracker, or make a list of them on your website, and advertise this list to your users. The ones that are interested in contributing will have something quick and easy to get started on, and you'll have that many fewer bugs to fix - it's a win-win! Ideally, once you have a system like this in place, people will feel more comfortable about filing trivial bugs too, and you'll end up with higher-quality software overall.
Don't require registration to submit a bug report
Trac is kind of bad about this since everybody runs their own instances, though if I recall correctly recent versions support OpenID, which is a big step forward. If I find a bug, but I have to go through the whole registration dance just to report it, I'm just not going to bother reporting it unless it's a really severe bug. You may say that I'm not a serious contributor if I let a registration page stop me, but that's kind of missing the point. Casual contributors can be just as valuable as really serious ones, and there are a lot more of them out there.
Allow editing through a web interface
This one doesn't actually exist yet, but it could. The normal process of submitting a patch involves checking out the source code, making modifications, generating a patch, and submitting that to the maintainers of the program. 3/4 of those steps could be automated on a code hosting site such as SourceForge or github or bitbucket. The code could be cloned on the server; the user could be presented with a simple text editor in the browser (or something more fancy, like Bespin), the user could save the code with a commit message when they're done, and the commit could automatically be submitted as a pull request on the server. I wouldn't want to use this to make serious changes to the code, but this isn't designed for people that are already making serious changes. For somebody who's just making a small cosmetic change, this would be a huge timesaver, and that in turn increases the number of contributions you get.