First you need to enter cockpit (if you don't see "Enter Cockpit" under Control on the right hand side below your avatar, go to "Position" and move until you reach the cockpit, then Enter)
Once in the Cockpit page, hit the Travel button
Umm, that's as far as ah can take you going from memory alone (currently traveling through Hyper so can't refresh the steps)
Getting to orbit is not the most intuitive of steps. After hitting travel, the default option is the city screen (or whatever level you are at - right now it should be city), which includes the Ascend button to get you to atmosphere. However, to get to obit you'll need to go to the Planet screen once you arrive at the atmosphere level.
Your faction should be able to provide you with further piloting help, or more in-depth instructions than those given by Tiali and I.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."