The venerable tradition of the sample, of the break beat -- a tradition that largely accounts for the origin of hip-hop music -- has been denigraded by lazy, inept, and uncreative practitioners. Many of those instances of lazy, uninspired sampling saw great commercial success, which in turn gave an impression to the masses that 'sampling' is when a hip-hop artist (like say, oh, I don't know, Puff Daddy), steals and recycles a song that was already a hit. Of course, this is precisely what Puff, and others of the same mold, did in fact do. The trouble is that this left an impression of sampling that is false.
Sampling can be done poorly, but it can also be done brilliantly, and it is a legitimate artform. Being a total layman when it comes to music, and only slightly better when it comes to sampling, I'm probably not the best person to explain this, but I know enough people (mostly older) who don't respect hip-hop or the art of sampling that I felt obligated to call attention to the creative and artistic aspects of the practice. Here are a few things that the best samplers and beatsmiths do which the hit-jackers do not:
Crate-digging is a term that, obviously enough, refers to the practice of scouring large collections of vinyl (most often soul, jazz, and funk records, but anything is fair game) for dope and elusive samples. Finding a nice piece of music that is easily recognizable, or is from a well-known artist, is already less imaginative then someone who goes diggin' in the crates and unearths an obscure gem. And once you find a choice record to sample from, there's still the matter of which part of the track will work best as a beat, and having the ear for this is a talent in itself.
Chopping is manipulating a sample in a way similar to how a DJ might scratch a record, only chopping is typically done to create a 'loop' of music, often in 4-bar time structure which often repeats for much of the song. It's not easy to describe, so for an excellent example of first class chopping, listen to Memories Are Here To Stay by The Intruders, and then listen to what DJ Premier did with that sample on Common's Sixth Sense (and for extra credit check Here's What's Left by RJD2, which samples the same record in a much more straightforward manner, and without chopping, but also creatively and to good effect). But what Primo does with the record is so uttetly brilliant, you might not recognize the source of the sample even if you loved The Intruders! Though the art isn't primarily in disguising the source, but in the resultant piece of music, and if you can't see the genius and beauty in The 6th Sense, then hip-hop wasn't made for you.
Included as a sub-category here I should mention other aspects of manipulating the sample itself, such as filtering the sample, speeding it up or slowing it down.
Blending is another art that originated with DJ-ing. When DJ-ing it's the act of attempting to mix one record into another. Kind of like a musical segue. When crafting a beat from multiple samples it means making them fit together in a seamless and dope-sounding fashion. It can also be done as a transition between tracks on an album (for some superb track-to-track blending check out Saigon's latest record).
Just as you might suspect, layering is the art of adding elements on top of a sampled loop. Whether it be the bass and drum tracks, another sample, a synth or live string instrumentation, multiple layers can give a track a more robust, dynamic sound and is another artistic tool which beatsmiths can use to make a track more original. This practice isn't part of sampling per se, but it is something that is done to samples to transform them into something fresh and different.
Hopefully this has given you a rudimentary appreciation for the craft and art of sampling. If your perception of sampling was that it was simple musical theft, I don't blame you. If you've gained an interest in sampling there's no better way to further that appreciation by listening to some of the greats at it; RZA, DJ Premier, Pete Rock, Havoc, Large Professor, Alchemist, No I.D., Blue Sky Black Death, and many, many others.