To get over the fear of working on other people, call ALL of your friends (even the ones that don't wear makeup!) and set up a day where you do their makeup.
Do your own makeup first, set up all of your product and supplies, put on your brush belt, and do your thing! One of the most uncomfortable things about doing makeup on someone you don't know is having no idea what they want, and no idea who they are. So you can start out by talking about what products they currently wear, their skin type, their jobs, etc., and those kinds of things will not only give you valuable information about the people you work on, but also get you and your client more comfortable with eachother.
Remember, practice makes perfect, and communication is key. Of course, as in any line of business, you will always have a percentage of people who aren't satisfied with their service, but sometimes it simply can't be avoided. But if you practice on your friends, maybe even your friend's friends, then you can gain some of the skills (not just makeup-wise) to go in to your new position and feel confident about your skills - all of them! Good luck!