It's likely that a ceramic disc has worn(could be either hot/cold) or could be debris within it, preventing it from fully closing.
The tap indicators red/blue discs on top, normally can be gently prised off using a small flat headed screw driver. This should then reveal a screwhead that will require undoing. But it maybe that there is a small screw or allen nut on the lever that needs loosening.(so check for that before prising red/blue disc off). Once undone the tap lever will be loose and can be removed. Under the lever is the tap valve mechanism (cartridge).
You will require a correctly sized spanner to remove this from the body of the tap. Integral to the cartridge is a ceramic disc, in some cases it is possible to replace the disc, but often straight swap out with cartridge is a better option.
Before you start removing any components, isolate water supply and have a small container handy for putting the bits that you have removed in, so they don't get lost. Also put the plug in the sink, so nothing finds it's way in to the waste, if dropped.