Every tattooist has their own preferred methods for aftercare of your tattoo, and indeed over time, you will develop your own. As a general rule though, this is the advice I would give.
Your body has its own ways to heal itself, but there are a few things you can do to help the healing process along.
I always advise washing the tattoo with an antibacterial soap such as Carex, with clean hands.
Next apply a thin layer of Savlon skin healing cream or Preparation H to the area.
Wrap the tattoo in cling film. This helps because you are not letting any air to the piece, which keeps it moist and therefore stops the majority of the scabbing, healing the tattoo from the inside outwards.
Repeat this twice a day for at least four days and avoid obvious things like sunbeds and swimming pools.