The regular way of micing cymbals on (R'nR) drumsets is by using OverHeads (OH)
Usually a set of 2 comdensator microphones.
It depends on how many cymbals and their placement, how you best place the mics.
The exact placement is highly a matter of engineer preference I think: I'll describe what I do.
With a standard R'nR kit, I usually place the 2 mics roughly 50 cm apart, 2 mter high.
I place them above the rim of the toms facing the audience, point them backwards roughly at the snare, slightly outwards. This way they're pointing away from most of the instruments & monitors. Some prefer them very close together, some more pointing to the cymbals...
I place them so high because that way, I can use them as 'natural reverb' channel of the rest of the kit, giving it more air. This depends on stage volume: I mic loud bands closer(lower).
If there is only one Ride & one other cymbal, I tend to place them closer & more direct.
I even dare to skip one OH to make the looks cleaner on a small kit.
If you've channels to spare, a separate condesator mic is placed close to the bell of the Ride cymbal, sometimes underneath.
If you have a lot of channels to spare, you mic every cymbal separately, but that's more Metallica-level.
My preferred pattern is Hypercardioid.
Microphones with large membranes are used sometimes, but I prefer small membranes (KM184).
Another favorite on riders is the AKG 414
As a basic starting point for equalising:, I turn up the Hi-pass filter to 400Hz.
Afterwards I sometimes tweak the high mids to remove 'tube-like' sounds, the high shelf turned slightly up.
I usually place condenser mic roughtly 5 cm above the HiHat, pointing to the bell.
Roughly the same EQ as a starting point.
The high mids of an HiHat sound totally different from other cymbals.