You can create orbits a number of different ways:
1
You can load up the Earth & Moon system file which already has the Moon in orbit around the Earth.
2
You can get a body (planet, moon, star, galaxy etc.) to orbit its parent (a more massive body) by right clicking on it (which opens the control panel) and then in the Commands group clicking the 'Orbit Parent' button. In the control panel under View Controls click the "Relation" button to see lines drawn between a body and its parent.
3
You can do this for all bodies at once by clicking "Orbit All" under System Commands (in the control panel).
You can get some interesting results by loading up a Galaxy or a ringed planet (like Saturn) and clicking "Orbit All" since the new orbits are in different directions.
You can also try introducing a larger body in "Cosmic Billiards" (under Fun Things to Do) and then command all bodies to orbit its parent.
4
You can also manually introduce new bodies into the system at the right position and at the right velocity to achieve orbits. You can learn about adding new bodies in "Learn the Basics" under Help on the Main Menu. (Press ESC to see the menu)
There's currently no easy (and mouse only) way to lock your focus on a planet or star and then rotate the camera 90 to launch the new body parallel to the focused body. It’s on my long list of feature ideas.
You can lock focus on a body. Use the arrow keys to slide the camera over, and then launch bodies, but it's hard to tell what angle you're launching them relative to the focus. You can see what velocity existing bodies are traveling around their parent to get an idea of what velocity you should set.
5
You can create a rings of orbiting particles by adding a Ring. Right click on a body and in body commands set the Ring Type and click the Rings button.
Try adding Geosynchronous rings around Earth.
6
You can also edit the system files and use commands to automatically calculate orbits. From the main menu click New and then "Create New System File" for instructions on what to do.
Let me know if you have any more questions.