In case you are more or less experienced with graphic software and feel yourself gifted enough to express an idea or thought through graphic image you may try yourself in designing logos for online companies. Skillful specialists are always on demand with their talent and creativeness. If you have basic HTML knowledge or web programming skills, you may go more deeply into it, and your work will be rewarded, but for creating logos you just need your talent and graphic software knowledge.
You can try yourself with lots of free to try software, giving you templates to work on them, giving you necessary knowledge of how this work is performed, like, for instance AAA logo software. With it you can get more experience, develop your skills, encourage your creativeness and prepare some works that you will show your future partners as you own portfolio, which is needed for your presentation.
You need to pay your attention to various types of technologies, learn how to use or combine them. For instance, using Flash may be of much use to you, and may stand you in good stead for other online activities. Try various fonts, and experiment with their colors and sizes to find your own unique style. Test combining pictures and text, use various directions and do not forget to be creative, this is what is most demanded in designer's works.
As for offering your services and finding clients you may use numerous online sites offering services for freelancers. You may use sites specialized in this field or use resources of more general orientation. Such resources are a good way for the client and designer to find each other. Of course, if you spend some time for creating your website with you presentation and for promoting it would be useful for your work. Just start with simple things and continue to move to serious business and you will succeed.