Follow the navigation buoys, and if you're hostile to the Alaska IFF there (everyone except Liberty lawfuls and Ageira), good luck dodging all the shots. There's also an easy-to-access jump point in Thuringia near Planet Gotha that can be traversed from Dresden.
Easy, Enter with your ship, thrust and use CM for missiles, follow the nav buoy, when you see prudhoe in radar, turn left, then, when you see junction turn right, go at thrust speed and that is done, everything is fun in Alaska, and it is simplier than you think, do not try bring transports, those are kinda junky (but a medium transport could be excel in passing by without much trouble ... just get a transport can sustain lots of damage (avoid the red plasma shots) and be agile enough to make the AI miss a lot of shots on you.
Good luck!
Ah, another thing, when you reach Earhart your exits are on the left side, right side there is the uncharted (up to freighters) if you take on uncharteds, make us a favor and save your entrance (because it is randomly and not showed on map) so you can return nicely and safely to earhart and so ...
Another tip, don't go the center of the map (keep always 30-40K or so) or the alien base will hit you and hit you hard! 2 shots maybe 3 and your ship will blow up
