One important thing to remember is that heat doesn't cause damage until around 140% heat, so you have plenty of range to play around in.
v 1.2 Update: The new heat mechanic in 1.2 has moved the heat goalposts around, meaning you now start taking damage to modules at 100% heat[1] and damage to your hull at 140% (or the second line on the new heat bar).
[1] - The point at which you hit 100% in 1.2 is the same point you would have hit ~140% in previous versions, so you are not at a higher risk, it's the measurement that makes more sense.
Video Guide
The video guide is still relevant in 1.2 and higher, just bear in mind the above about the heat numbers. i.e. don't go above 100% any more.
How I've always done it
The way I usually fill up my tank is to aim first, have the star just on the edge of your view then throttle down to zero. When in supercruise this does not mean stationary so adjust your angle in small increments so that your heat stops rising but you are still getting a decent rate. If you are in a hurry, adjust your speed up in small increments as well which will give you a better rate but increase your heat, so you have to keep watching.
When scooping a lot of fuel, there's not much you can do about it other than find a good angle then go read reddit whilst you scoop.
Rate vs Scoop size
Each size and class of scoop will have a different rate and finding the optimal for your currently fitted scoop will take some experimentation. As above, until you know what a "safe" rate for your scoop is, just slowly increase the rate by adjusting your speed or angle against the star until your heat stabilises at a value less than 100%.
Most of the populated space is near Sol. You can direct your ship towards Sol by moving towards the 0,0,0 coordinates on the Galaxy Map.
Otherwise you might be able to find nearby populated systems on the Galaxy map by zooming out and playing with the View filters - anything with an Economy likely has a station.
Best Answer
Call the Fuel Rats!
The Fuel Rats are a group of players that will race to bring you fuel. From what I've heard, it's not uncommon for a few of them to all try to converge on your location as fast as possible (competing to get credit for your rescue). They've been known to go to extraordinary lengths to help out stranded players, with a recent 3600 light year 6+ fuel rat relay rescue recently described in GalNet News.
You can call for them via the IRC on their website, via /r/FuelRats, or by posting on their thread on the official game forum.
Here's Fuel Rats' current instructions for those waiting to be rescued:
There's a couple other smaller groups that do the same thing, but Fuel Rats is the biggest, best known, etc.
If you'd rather, you can get a friend to help you out instead. (The one time I got stranded, it was somebody in the group I was playing with that came to my rescue).
Your friend would need to equip a ship with a Fuel Transferer Limpet Controller, Cargo Racks, and a supply of Fuel Transferer Limpets/Drones (under reload/munitions after buying the controller). Your friend will probably want to equip a Fuel Scoop and additional Fuel Tanks.
"Fuel Limpets" are a drone stored in the cargo hold and controlled by the Limpet Controller. They can transfer 1 ton of fuel, (and then self-destruct) from the ship with the controller to another ship. A higher class (larger size) controller can handle more limpets at once, and increasing either class or rating increases the range at which they'll operate.
Procedure is something like this:
Before the 1.3 release on 2015-06-05, you would be dead and might as well self-destruct.