Isolating the kick from the rest of the kit takes a simple brute force approach: After setting up the ussual internal mic on the kick, and applying whatever internal damping to the heads (pillow, folded up blanket, whatever), you cover the kick all around with heavy blankets to muffle it. Front, around the shell, and back, leaving clearance for the batter to hit. You get less of the kick in everything else, and you get less leakage from the snare into the kick mic. Having tried various balances over the years, I have gravitated to a 9 mic balance: overheads, kick, top and bottom snare, hat, and one for each tom (assuming the usual 3 tom kit). For those who as why so many mics, it is because the most commonly expected rock and roll sound uses surgical EQ on each drum, taking out unwanted sounds while accenting the fundamental and the attack. Back in analog days I did this when tracking. Now I do all the EQ on playback, which means the drummer doesn't have to bang around while I get EQ settings.

Now, if you are lucky and the drums sound just right live in the room (meaning the sound you want in the final mix), you can go with fewer mics, provided, that is, that the drummer givew you a good level balance between the drums and the cymbals. If you get a "basher" though, just mic everything and get the balance in the mix. Yes, I know some great rock records were done with fewer mics (early Zepplin), but there areother big ones that went for much more than I use (I saw an article long ago that showed the track sheets for Heart's "Magic Man", which required a 2-machine lockup for all the tracks, now a few of which were for drums). So one could argue both sides, but I don't risk it when working with a drummer who is now to me (which is most of the time). I keep my options open with multiple mics and tracks, because I don't want to be going back for a "do over".