Welcome to BHW. There are many services you can offer that can make $10 a day without investment. You could try article writing, web design or programming. You could sell these services on fiverr, on forums or freelance sites such as freelancer and odesk. Remember those kind of services most likely won't be making you the big bucks so make sure you keep researching methods, niches and techniques to help you grow your knowledge and create long term projects. Some advice I'd offer you is to save say 50% of your money for yourself and invest the other 50% in another project or niche. Remember that if a method isn't working first time around, you should keep at it and trying to promote your niche in a different way. Not all methods will be guaranteed get-rich-quick schemes. Good Luck!
TL;DR Services such as article writing is the easiest method without investment.