While I'm no expert, I've done this several times successfully with various beers. Some folks will tell you that the yeast isn't the same for various reasons but I'm not one of them. I'm just going to provide a quick method, i.e. what works most of the time (without a stirplate).
1) a. Clean the bottle of beer you're going to be taking the yeast from well. You can use isopropyl alcohol to wipe it down or use some other method. While you're at it, clean the opener and a 6" X 6" piece of Al foil. Set the foil aside.
1) b. Make up a low gravity starter mixture, 1.030 or so will work, by boiling up a little DME and some water. It doesn't have to be a lot but you will want somewhere around a pint or so. Allow this to cool (or cool it yourself) and put it into a sterile container, like a boiled quart jar (and while you're boiling the quart jar, go ahead and boil the lid and ring). Set all this to the side.
2) Open the beer and gently pour your beer into a glass but don't touch the lip of the glass with the bottle. When you get most of the beer out, stop pouring. The goal is to NOT pour out the yeast into the glass.
3) Go around the lip of the bottle a few times with a flame (Bic lighter or the like) to sterilize it.
4) Here is where a few people will disagree but... Carefully pour about a quarter of the starter solution you made in 1) b. into the bottle. Swirl this around to break up the yeast sediment at the bottom of the bottle. I find this allows more yeast to be gathered than simply swirling the yeast and what's left of the beer...
4) Alternate method... Swirl the beer to break up the sediment.
4) Alternate method... Pour in about a quarter pint of pre-boiled water into the bottle and swirl this around... Make sure to calculate this into your gravity calcs so you don't get too low.
5) Pour the mixture from 4) (whichever method you do) into your clean quart jar from 1) b. Put the lid back on and swirl it around well to mix it up.
6) Remove the lid and put the tin foil on top of the jar. Squeeze the foil around the neck. Now, put the ring over the foil to hold it. Alternatively, you can use a rubber band or nothing.
7) Now, every few hours or a few times a day (as often as you think about it or can), swirl the mixture. In a day or so, you should notice a little foam or perhaps some bubbles. This will mean it is working and the yeast is viable. You can then step up the starter to larger containers to the level you need to pitch... Give this at LEAST 3 days to work. If you don't have anything after 1 week, chances are you didn't get enough (or any) live yeast.
NOTES:
Imported beers are harder to get anything from than domestics, generally.
Some beers are pasteurized and have very little chance of actually producing a viable starter.
Cleanliness is very important.
It may help to put several beers into the starter solution at once (i.e. open several beers in one evening and put them all into the solution).
Some breweries use a seperate strain to bottle condition. Some breweries claim to...
There are more ways than this one to get a viable starter.
Again, this is my experience. And again, there are several reasons this may not work or may not be what you should be doing but I won't go into those...
Hope this helps!