Click on the File selection on the menu bar, and then choose "Load System". You will see a number of sample Gravitorium files, which always have a .grv extension.
Choose "Earth-Moon.grv" and click on OK.
To start with, you won't see very much. A small circle in the middle of each of the three display windows, and on two of them a separate dot about halfway to the right of centre. Labels show you that the circle represents the Earth, and the dot represents the Moon.
Click on the 
(start) button at the top right of the main screen. The simulation will start.
You should see the dot representing the Moon circling the Earth. If the simulation runs
reasonably quickly on your system then you might want to slow down the speed (use the slider underneath the heading "Speed" towards the lower right of the screen).
Once the Moon has completed one orbit, click on the 
(pause) button. Note that Gravitorium
has accurately predicted the length of the month at around 28 days. The top left display
window should look like this:
Notice that the circle of the Earth has become blurred. That's because the Earth doesn't stand still while the Moon orbits it - in fact both the Earth and the Moon in reality both circle around their mutual centre of mass. This point isn't exactly at the centre of the Earth, but it is nevertheless below the surface of the Earth. So it seems as though the Earth is just wobbling a bit. After enough orbits of the Moon, you'd see that its orbit too would appear to become a little fuzzy for the same reason.
With this simple simulation, you might just want to play a little with the controls.
For example, click on the "Label" button to see labels next to the objects. Use the "Clear" button to clean off the trail marks.
Now for something a bit more sophisticated. Click on the "Centre" combo box - you'll see "Earth" and "Moon" listed as well as "Grid Origin" and "Centre of Mass". Select "Earth" and re-run the simulation. It will seem pretty much as before, but this time the Earth and the Moon's orbit won't become blurred - that's because the display is now centred on the Earth, so you don't see the absolute movement. You could try centering the display on the Moon - from here it looks as though the Earth is circling the Moon.
OK. That's it for the very simple simulation. Now let's try something more interesting.