you have 2 types of travel one for in system travel and one for hyperspace
if it is in the same system, then you just take on the mission then leave the startport / orbtal platform and on your left hand nav panel your destination should show up in blue. select that and once you are far enough away from where you left press J it will fire up your drive.. generally for starters you can fly straight to destination, , you will get a countdown on your distance, once it gets to 7 seconds make sure your throttle is in the blue zone.
when you are close enough it will come up on yourscreen to disengage, press J again.
get close to detination (7.5km) and in the left panel request docking and hopefully profit.
IF its in another system if it is 1 jump that is easy, if it is more than 1 jump you need to go into your galaxy map and select the system the mission is at and click select route....... you will have to play around here as i do it automatically and cant remember how i do it. the select route icon may be a double arrow pointing left and right but not sure.
take off, fly away from the starport, select the blue target, this time it will be a different system (will be a number of light years away rather than light seconds) once far enough away from the space station this time press H for hyperspace, you will jump, and then when you come out you will be heading to a sun, be ready to pull up to fly past it, then in your left panel select... nav panel i think it is look for blue makrer and select your destination.
by the sounds of it you got too close to the sun, this is ok you will be in normal space now, floating near the sun...... turn around and fly away from the sun, once you leave masslock and your drive has cooled own (after an emergency drop out your drive is offline for maybe a minute) then press J.
you will get a blue escape vector appear on your hud in front of you, aim for that wait for your drive to charge and cross fingers.... at this point your ship will likely overhead, dont panic, it sounds bad and lots of smoke but you can get pretty hot before you die. ignore the alarms, once you get to supercruise after a few seconds your ship will start to cool down, fly away from the sun, look in your left panel, target your blue destination and do as above........ it may be you have to make more than 1 jump, if you do, then your blue marker will not be your final destination but another system (it will be LY away not LS away), that is ok, press H and jump, this time being ready to dodge the sun.... hope you dont run out of fuel,
always refuel when you land, you may want to get a fuel scoop.
that sounds complicated, its actually easier to just do it, or watch a vid of somene doing it, there are lots of guides.
HTH and fly safe cmdr.