Hyperspeed is a really cool thing in LotJ. It also is your only means of traveling between systems. Each system contains a different planet, so to get anywhere, you'll need to know how hyperspace works. However, there is a little prep work that goes into it. The CALCULATE command should show you different planets and how close or far they are from you. Your ship has enough fuel to make it to the ones that show up in green text. Your ship will have to land and refuel at least once to make it to the ones that show up in red.
The PLANETS command should show you the planets and the systems they're in.
Once you have determined which planets you get to via hyperspace, and selected the planet you want to visit, you need to find out how to get there! Use the SHOWPLANET (PLANET) command to find the coordinates of your selected planet.
To calculate a jump to a planet, subtract or add 500 to one of those coordinates. This makes sure you don't fly straight into the planet from your hyperjump. Then, input CALCULATE (PLANET) (X COORDINATE +/- 500) (Y COORDINATE) (Z COORDINATE). This will begin the calculations for your jump. Depending on how far away the planet is, it may take some time to prepare.
You can't jump out of the system unless you are 500 units away from the nearest ship. Use the proximity command a few times to see how close/far you are from the nearest object. Once your jump has been calculated and you are clear from all obstructions, enter the HYPERSPACE command to start your jump. In hyperspace, a count-down will appear of how far away you are from your destination.