How close together you make your lines of stitching will depend on how you want your finished quilt to be -- really close together will result in a stiffer quilt; the farther apart your stitching lines are, the softer your quilt will be. The kind of batting you use will also determine how close your stitching lines need to be; check the instructions on the batting so you'll be sure to quilt it closely enough.
I've found that large meandering movements that kinda look like jigsaw puzzle pieces are the easiest for me to do. For me, a random pattern can cover up a lot; it's a lot easier to see my mistakes if I'm doing something with a noticeable pattern.
Like others have said, staying relaxed is important. If I find myself tensing up, I stop for a little bit and relax. It also helped me to draw on a piece of paper before I go to the machine so I can get the movements in my head, and I try to visualize where I'm going to go next before I actually get there (if that makes sense). Keep practicing and have fun!