====== Jumpdrive ======
Most ships in Unending Galaxy are fitted with a short range jumpdrive allowing you to quickly move from a location to another. The engine doesn't require fuel, but it however needs time to fully recharge. Jumping also takes roughly 10 seconds and during this process your ship won't be able to move. As such the jumpdrive is a traveling tool, not a magical way to escape from certain doom.
To use the jumpdrive, you can either press the button at the bottom of your left menu bar or use the keyboard shortcut, [J] by default. By doing so you'll get a view of the galaxy, sectors with a green overlay are the ones where you can jump. Left click one of them to start the jump procedure. And if everything went right, you'll see a yellow “flare” around your ship telling you the procedure has started. Do not worry about your followers if you have any, they will jump too automatically granted you're jumping at a sector that's not directly the neighbor of your current one (in that case, they'll simply move to the destination).
As shown in the above screenshot, flares are also displayed in the destination sector, making it easy to see if you (or your enemies) are getting reinforcements.
====== Warpgates ======
Warpgates are huge and costly structures built by the various factions and only one can be built by solar system. They allow you to immediately travel to any sector with another warpgate, granted the faction controlling the gate is not hostile. To use a warpgate, move your ship very close to it, select the gate with your mouse and press the [J]ump key (or use the button). Here again you'll be shown the galactic map and possible destinations are highlighted in green. Left click a sector to jump to the location.
By using both system cleverly it's very easy to move to any (colonized) point of the galaxy quickly. Also note that the AI use those system as well. Try to keep that in mind if you are raiding another faction's territory that look lightly defended.