I want to offer online personal training service. How can I get clients and promote this kind of personal training?

I have done it and I think a key to it is to constantly connect and communicate with your clients. Use phone, email and also software to stay connected. Software was actually one of the things that helped me most with my clients because you can both look at the progress and workouts and better manage it all on one site. Like others have said in-person is much better but online training is better than no training. One Idea is to supplement the online training with a few in person sessions per month. Not always possible but it really would be helpful.

Edit: Since some have asked about the tools I used, http://www.fitsw.com/ was the specific software I used the most. There are many other options as well but this one was free and worked well. This type of software really helped improved my success and client retention. My client's loved being able to track their weights and exercises online with me. The tool provided a suite of online tools like workout tracking & organizing, goal/body measurement progress tracking (in very nice easy to read graphs), diet plan creation, allowed me to provide demo videos for my clients and included a scheduling system.