Be warned, this is the "expensive gear" post. Many people here like to use pocket recorders; well this isn't about them. It's all about combining different "big" microphone types.
Tips & Techniques
1. Dual condenser/dynamic setup.
Dynamic and condenser microphones compensate for each type's deficiencies. E. g. condenser microphones usually love to record higher frequencies, whereas dynamic microphones all have a proximity (sometimes boomy) effect and are mostly sensitive in the low midrange (forget recording cymbals with a dynamic, unless it's a rare type designed to work like a condenser). So, the simple idea is combining both. A classic technique for recording a drum is placing a condenser (or dynamic) on top, and a second microphone (dynamic or condenser, though frankly dynamic microphones fare better as exhaust microphones) at the drum exhaust/bottom. This works for any sound source, though obviously you'd have to be careful about placement (dynamic microphones are less sensitive and need to be closer to the sound source than condensers). And flip the waveform phase of one microphone (usually the bottom microphone).
2. Long-distance recording.
This usually works better with shotgun microphones. Place the condenser at least a metre away/above a cymbal or instrument to be sampled. This obviously may pick up a lot of stray ambience unless done in an isolated studio/room, but it allows switching to a higher gain and therefore detail for a condenser microphone. Something most people don't know is that a condenser can actually be gained higher for higher detail, and placing it too close to a source (like immediately over a cymbal) can kill detail because the microphone will clip with less gain. Better place a sensitive dynamic microphone (something like AKG D-40, Audio-Technica ATM-650, etc.) immediately over the cymbal and a condenser farther away (overhead, but aimed at the cymbal). This gives more ambience/detail.
Try to visualise the sound as it's coming off the sound source. A soundwave sphere with its centre at the sound source. Placing microphones in points of highest intensity usually means placing a couple microphone with a 90-deg. angle, each microphone facing into the sound source at the top of a 90-deg. triangle. This does not always work, but usually picking up sound off two points like this helps.
Echoes aren't necessarily unwanted. Yes it's nice, it's very nice to have a treated studio or mini-studio where there're almost no echoes and all you get is the speaker sound and no outside noise for recording. However, most instruments are at their best with a sound body composed with echoes as well as the main sound. Which is why studios often have a brickwall or wooden patch, for adding presence to takes. In a small studio, just recording a shaker or some bells or tambourine above a desk can help improve the liveliness of an instrument, though it's best to experiment with microphone positioning and instrument distance from a stone wall or wooden panel.
5. Phase Alignment
...is very important, whenever recording with more than one microphone the resulting waveforms will be out of phase - albeit slightly, by a few milliseconds or samples. However, time-aligning both (or more) waveforms will reinforce the sound and make it more realistic. It doesn't always have to be 100% accurate, sometimes delaying a waveform by a few samples or milliseconds can produce a "fatter" sound. The general rule is that anything longer than 5 msec. time difference is usually perceived as a delay and not a "fatter" body.
6. Drum Shells
...can be recorded too. This obviously requires more than two preamps/recording channels (already used up for top/bottom), but it may add a bit more realism. Place a third microphone aiming at the drum shell rather than exhaust or skin.