It's both similar and different in the enroute world. As for how we determine a vector, we have a function that lets us take our cursor and click on any two points and it will give us a heading from the first to the second. It's not corrected for wind or anything, so we still have to guess a little, but it will give us an idea. Or, we can just guess, especially if we know your current heading. A third option is just to tell you to turn x number of degrees left or right from your current course.
For tweaking your heading, we can run out a line that shows up to 8 minutes straight ahead of your current heading, and if it isn't pointed directly at whatever you are supposed to be pointed at, we know. And some controllers will NOT be happy about it (I've heard pilots get their ass reamed multiple times over this), others won't care too much, as long as you didn't put yourself into a conflict with anyone else because of it. Just ask for it, unless there's a good reason not to, most controllers (that I know of) will give it to you no problem, then you won't have to worry about it. Of course, it all depends on the controller, and more so, how busy the airport you are heading to is. I assume you are talking about a smaller, not very busy place.