The short answer - Start by becoming an active user of the project. It will make it easier.
The long answer -
The problem isn't that open source projects don't want help - most would be happy to have all of the help they can get. The problem is that most people who decide to help stick around just long enough to take some time away from the development team, then "flake out" and never show up again.
I have been very active in a couple of open source projects in the past, and we ran into this all of the time. It was very easy to get people to want to help, but very hard to get them to actually put the effort required into the project in order to be useful. I personally spent many, many hours trying to help out new prospective developers, and nearly always ended up just watching them disappear.
The team will be much more responsive if you can prove that you're serious - and it usually takes more than just showing up in a chat room, forum, or on a mailing list.
First off, I'd start by finding the right project. It's easy to find open source projects, but more difficult to find the one that's the right fit for you.
This is the difficult, or the easy part, depending on your point of view. I'd recommend starting with a project that you are familiar with - and hopefully one you've used. If you find one you're interested in, try using the software in its current state before you even think about trying to join the development team. If you are a user of the software, it's more likely that you'll be interested in contributing over time.
Using the project will do two things -
One, it will familiarize you with how they are thinking about the project. This will often make it easier to understand the design of the code, but most importantly, help you understand the goals of the current team.
Second, it's also often easier to get the ear of a dev. if you have specific questions to ask. I personally am always very responsive to a specific, directed, intelligent question. This helps build a relationship with the current development team.
Once you've become familiar with the team and the project itself, and have some idea of what's there, try to fix one or two of the bugs. This is an easy way to show that you can be productive and useful, and will be received fairly well.
At that point, the team will probably be much more receptive to helping you find good, longer term goals and tasks on which to focus. I've had a couple of people who approached our projects more along these lines, and we've all been very happy to help them try to figure out how to fit in and mesh with the team as whole.
That's the goal - you don't want to just be a contributor in the long run, you'll want to be part of the team. That's when you start feeling ownership over the project, and when it really gets fun.