On a more practical note, the OP will have to decide the best way to start. As I mentioned earlier, few tutors attempt to go full-time straight away. Most require the security of guaranteed income from a language centre / school in the beginning. After that they can start to find private students.
Developing your student base requires a lot of effort in the beginning. Advertising and marketing yourself via all means is important (online, physical flyers, tutor agents, word of mouth etc etc). I'd advise trying to limit yourself to a geographical area in order to keep travelling time under control but I realise this is difficult to do in the beginning.
After some time hopefully you will have built up a decent reputation for yourself and then I would advise trying to make the shift from travel-out tutor to tutoring from home. This is a very important move to make if you want to earn really decent money and still have a sustainable and decent work / life balance. Many tutors can't / won't make this move and get stuck in the 30-40K zone that I mentioned in my other post.
Also, I can't stress enough what a difference it makes being able to tutor from home. It is like black and white when compared with travelling out to tutor. I've done both, and travelling out to a lot of students leaves you exhausted at the end of the day. Now, tutoring from home, I can easily handle 8+ teaching hours per day and still have energy for family and other things. The ability to teach in comfort, in a controlled environment and without wasting any time travelling can't be underestimated.