bath shower mixer tap dripping

If it's like the last one one I done, it's a grub screw behind the handle lever - that lever unscrews to allow access to the grub screw then the top pulls off allowing access to the ceramic cartridge below  - it was the hot passing for me but better to change both.

If you have isolators on the taps turn them off one at a time but you might as well change both cartridges anyway. 

The worst that can happen is that if the ceramic disc has cracked it might break completely and jam the tap, usually in the open position and you won't be able to turn it off. 

I would change the whole tap, fucking about looking for replacements for unknown makes is a nightmare, get a cheap one from screwfix, they give a 12 months quibble free money back guarantee if it fucks up,