Check the washers on the tap to assess if that is causing your tap to leak.
If it is the washer, simply tap the washer off and take it to your local hardware store to replace it.
If it continues to drip, reseat your washer.
If the crack is very bad, reseating is not advised, rather replace the whole tap.
The tap head may be stripped, which means only the tap head needs to be changed.
The mixer cartridge may be broken, which means the whole cartridge will need to be changed.
Each of these can be a DIY task. However, if you are not familiar with fixing any of these, contact a registered plumber.