How can I reach distant systems

The route planner now(since update 1.1) will path up to 1000LY away, and you don't need to wait for it to path before selecting.

Just select the star you wish to travel to and if it is within 1000LY you can click the plan route button and it will set one up for you quickly.

The automatic route planner still takes a decently long time to build a web, though.

If the line that appears is solid you can make it there in a single tank. if the path becomes a dotted line, you will need to stop and refuel or scoop some fuel to keep going.

There are some tools people use to speed up the searching, but as with any third party app. Use at your own risk/discretion.

I personally never bother with the 3rd party tools. They don't contain information about every star system in the game and there is no guarantee of accuracy of the information that they do contain.

I always do as you suggest - rotating the map around the destination so that I can see the marker for my current location (if you "lock on" to the desired destination you can use the little arrow buttons next to the destination and your current location to swap between them, giving you hints to the direction).

Once the spider web of routes has expanded out to the maximum range (currently about 100Ly), I choose a point on it that appears to be going in the correct direction. This system is clumsy, slow, and frankly not very good, but at least it doesn't involve Alt-Tabbing out to 3rd party tools.

Soon (within this month, according to their announcements), Frontier are launching an update which among other things will extend route planning out to 1000Ly, so this should alleviate the problem. Hopefully this range extension will not be a simple adjustment of the current route planning max distance parameter - hopefully better optimised path finding code has made this extension practical.

Personally I don't understand the need for the game to plan out every possible route from your current location. Like the original Elite, it could simply give an indication of how far you can travel in a single jump and leave it to the player to trigger the route planning - when they select a system as the destination, no matter how far away it is, the game should then plan the route to that system. It should be a lot faster, a lot less cluttered and a lot more useful.