I think the chances of a complete beginner (or most anyone else, for that matter) finding a more advanced person to compete with and teach them _for free_ are extremely low. Now, some people do it if love is involved, but still even then the two of you would need to pay for coaching from time to time from someone else, just because you need to have another pair of eyes looking at you. You can't really see yourselves when you are dancing, after all! Also, if you're a beginner and want to compete, you're better off starting with the best teachers you can find and afford, rather than having someone who might not be all that much more advanced than you teaching you. Bad habits or improper technique learned early on are more difficult to break later. You might as well start out learning from someone who has lots of experience training other competitors, and people with that kind of knowledge and experience aren't going to be out there teaching for free.
Your best bet is to get into the mix and start taking lessons, looking for a partner all the time. That way you can learn together and split the costs. Take group classes as a way to get an introduction at a lower price, and also as a way to meet people. Also, there are many different styles of dance, so if you take group classes you can sample the different styles (Latin, Rhythm, Smooth, Standard, Salsa, Argentine Tango, West Coast Swing, Lindy Hop) and see what you like the best. When you find the styles you like the best, concentrate on them. This way you'll get the most for your money. Take private lessons too, when you feel ready for them and when you can afford them, because the individual attention you get will help you really understand what it is you're being taught in the group classes.
Good luck! The first step is to just get out there and into a class somewhere.
