Using samples made by other people by saving samples out of their mods is generally known as ripping. There are a million conversations about the ethics of this practice, and still no end in sight to the endless debate about it.
However, as you will find out, there are more than enough sample sites out there (with decent samples) that ripping shouldn't be necessary.
Just about any tracker enables you to save the samples in a mod. So all you've got to do is load the song you want a sample from into a compatible tracker and save it. There are other programs that enable you to rip samples from mods too, one of them being DMPC, Dual Module Player Companion by Brad Meier of Psychic Software, a mod player shell for MS-DOS. While most trackers save samples in their own proprietary format or as raw MOD-compatible samples, DMPC saves to WAV/VOC/RAW.
jester wrote in 1998: If you don't have a tracker or a ripper, you can still obtain the samples in mods by loading the file into a sample editor capable of loading raw sample data. You will have to set the number of bits and style (signed or unsigned) according to the format you're loading (MOD is signed 8 bit, S3M is unsigned 8 bit, for example). You will be presented with some static, which is the header and pattern data, followed by the samples in the mod. Any decent sample editor should enable you to cut out the individual samples. The next step would be to get the sampling rate right, otherwise the samples will sound off key when used. MOD samples generally use a sampling rate of 8363Hz for a C in the second octave, so try this for starters (or an integer multiple). The more advanced formats with variable CxSpds pose more of a problem, you're basically left with your ears and perhaps a musical instrument to get them right. Note that a lot of MOD samples are not tuned to C. Quite often, an A is played instead when a C should be. See appendix H for a table of note frequencies to help you calculate the appropriate sampling rate for transposing wrongly tuned instruments.
Glen Warner <email@example.com> adds on 4/28/98: On the Mac, you don't need a special program to get samples out of a mod. You simply open the mod in your tracker of choice, select the sample you wish to save, and save it.