Mixer taps are common in kitchens, the one below requires a few turns of the tap handle for the water to run fully. Some newer kitchen taps are 1/4 turn taps and use cylinders rather than washers.
1.The spout. If water is constantly dripping from the spout then one of the washers is probably faulty. To find out which one is leaking you can isolate the water to each side of the tap. Once you know which side is leaking you can replace the washer as described here- Replace tap washer
2.If water is leaking from below the tap handles then the sealing ring is probably damaged and could need replacing. Instructions on how to remove the head gear can be found on these two pages Replace tap washer and Replace tap head gear for a better look at the sealing ring you can look at repairing a tap head gear .
3.If the water is leaking from the swivel base then you may need to replace one or more "O" rings, this is described below.
Some of these mixer taps have a small grub screw either at the front or back, this needs removing before the spout can be removed. This particular model does not have a grub screw and you remove the spout by turning the spout to line up with the taps and then push upwards.