There are primarily 4 ways to deal with mic bleed, and sometimes none of them are practical:
1. Use EQ going in, or in post production. A lot of people, for instance, will use bass cut on the overheads to reduce bleed from kick and toms. They will cut highs on kick and toms for the same reason. This can help when the sounds you are trying to separate are clearly in different frequency ranges. It won't do a damn thing about voice and guitar, for instance, which share frequency bands. Others hate it, because they really want the overheads to pick up the whole kit.
2. Use physical isolation. In other words, the recording is live, but the mics are in different rooms. I often use a "monster in a box", a big mucking plywood box lined with carpet and acoustic foam. The guitar amp is bolted inside with a mic, and the whole box is placed in another room. This means you need a lot of space, and everyone must wear headphones. You also need a good headphone amp with a lot of channels, and a bunch of headphones.
3. Record by layered overdubs. Start with a scratch track of the guitar and vocals. Then lay down bass and drums with bass going di. Then erase the scratch tracks, and add the other parts one by one. This requires musicians who are versatile and flexible, as well as skilled. It works for recording artists, not bad dance bands.
4. Use a noise gate. Often they come as a set of 4 (a "quad" noise gate). This can be hardware or software. It will have parameters- range, threshold, and release. The threshold determines how loud something has to be to get a signal through (in other words, to open the gate), Release, like on a compressor, determines how gradually or abruptly the gate will close when the noise level drops below the threshold. Range determines how much noise reduction the gate applies. In other words, is it a 4" thick oak door, or a screen door? The downside-The higher your threshold, the higher the range, and the faster the release, the more obvious it is. For something abrupt and fast, like toms, fairly high threshold and range, and fairly quick release time can be used. For something like voice or crash, it has to be pretty subtile, or it will suck. Right now I'm recording a radio play with multiple voices in a live studio setting. The noise gate is my friend, as long as it's used gently. If you accept that the gate can't get rid of all the bleed, you can get it to reduce a lot of the bleed without being obvious. There are, of course, software plugins that do the same thing. Even my little Kord PXR4 has a noise gate in it.
Hope this helps-Richie