Going out on your own is a decision to not take lightly. Leaving the security of a steady job is scary. Many people in a situation like yours start out by moonlighting on the side to test the waters and/or pick up some extra cash. You get the best of both worlds - the security of the 9 to 5 (or 6 to 6 in many cases) with benefits, insurance, and the like - and the flexibility of working on what you want to on the side (and extra cash).
I think that getting started in any field on your own requires contacts; knowing the right people. If you have been in the industry for any amount of time and are active in the community, chances are you have contacts. You have to use these. If you aren't already on LinkedIn, get on there and develop contacts with old coworkers, college friends, anyone who may be able to use your services or know someone who could. Never burn bridges, people can always roll back around years from now.
One thing to be careful about if you do decide to moonlight on the side is whether or not your current employer has a policy regarding working on the side or having a second job. Check into that with your HR department. You say you work for a large company, I bet they have a policy on this.
There are many books out there that can help as well. Many freelance books are geared toward the "creative" industry - graphic design, artists, photographers - but the principles are the same and apply. Here are a few to check out:
Both of these are pretty easy reads, but very informative. They contain info on getting clients, getting paid, tracking time, self-promotion - all important topics.
As far as getting your foot in the door, often your first client could be your former employer - they know you and how capable you are. That's if you go our cold turkey and leave the day job. If you moonlight, look into former employers, environmental consulting firms, small shops that might need GIS but not on a full-time basis. If you work in a specialized area, you will know what type of shops to seek out. I worked in the oil and gas industry for a while, so I went to small oil and gas companies and consultants to see if they needed my services. Some did, some didn't - that's how it goes.
Get good a shameless self-promotion, you'll need to do it. Craft an elevator pitch about what you do and what you can offer someone, as you never know when you will run into someone and only have a few seconds to capture their attention.
This is a very difficult topic to cover all of the bases on here, but those are some of the more important ones that I have come across.