Madaba's advice is great. You should follow all of it (and particularly the part about trimming the wick before lighting and only lighting when you have enough time to let the candle burn edge to edge) But I take one more step to get full life out of my candles.
If I still have wax in the container after the wick has burned away completely, I will remelt the wax and add a new wick. I do this in one of two ways depending on the container. One option is to place the container in a small pot of water on the stove and turn the heat on low. The water level should be slightly above the level of the remaining wax in the container, but should not be so high as to allow water to enter the container. That would ruin the wax. Be careful with the heat. If you turn the heat up too high or if the water becomes hot too quickly, you risk cracking the container. And if the water reaches boiling, turn the heat off completely and let the hot water do all the work. Once the wax is fully melted, drop in a new wick (take care to center the wick), allow the wax to cool and completely harden over the next two hours, and then trim the wick to within 1/4" of the surface of the wax with a pair of scissors. If you have a lot of wax, you may find you have nearly 1/3 of a candle remaining and once the wax hardens, your candle will look almost as good as new, with a smooth, creamy surface.
Another option is to scrape out the remaining wax, place the wax in a Pyrex measuring cup in a pot of boiling water (basically using the Pyrex cup as a double boiler), and then repour the wax into the original container with a new wick once it is melted. You can also pour the wax into tealight containers if you prefer.
If you want to go the tealight path, simply buy a pack of inexpensive, unscented tealights, remove the tealight candle from the tealight tin, remove the wax from around the wick, (so now you have just an empty tealight tin with a wick sitting in the center) and pour your candle wax into the empty tealight containers. Now you can use that great, expensive candle fragrance in any container you like.
Wicking a candle is a science. Finding the perfect wick for any given wax type in any given candle size takes much research. But I find that an HTP 73 prewaxed wick works reasonably well with most regular sized (Diptyque sized) containers. These wicks come with a base attached and usually run about 10 cents US each and can be found at craft stores and on eBay. Well worth the tiny 10 cent investment if you purchase a lot of high end candles.