Note that while this may sound like a lot of complicated
mathematical mumbo jumbo to you, the aspiring
Britney Spears remix artist, the reality is that you just import your sample into your multitrack audio application of choice (
Pro Tools,
Sonic Foundry's
Vegas Audio,
Cubase's
Logic Audio,
Cakewalk...), route the channel with your sample to an
effects plugin, select the time stretch/pitch shift plugin of your choice, tell it how much to stretch, and you're good to go. It's remarkably easy.
In fact, one application, Sonic Foundry's ACID, does automatic real time pitch- and time-scaling for every sample you use, according to a tempo and key you set, with remarkable results. It's not the slickest algorithm I've heard, but it is computationally lightweight, and sounds good enough that for moderate amounts of shifting most people will never notice a difference. Plus I believe they use a better algorithm when you render your track to an audio file.
Time- and pitch-scaling software hardware is incredibly useful, and the market today contains a very clear spectrum from inexpensive consumer products to high end, professional products with high end, professional prices. The current king of software plugins is Serato's Pitch N Time 2.0.1, which will run you USD$800, comes only in AudioSuite format, but produces breathtakingly clear results. Roland also has a newish sample playback synth, the VP-9000 Variphrase Processor, which does DSP-based realtime tempo- and pitch-matching, as well as bends and other, more synth-y, manipulations. To take one home, however, will set you back about USD$2500...