I've got three friends who are tattoo artists, my wife has about 15 tattoos and I've got a few myself.
I'll tell you what is most effective in terms of not messing up your tattoo, not what doctors recommends or some standard tattoo artist advice
Keep it wrapped up for the first day and night or two (yes it traps in moisture and some sweat but it's still the right thing to do).
2-3 times a day change the cling film, when it's off - if your tattoo is very clammy or bloody - you can let some lukewarm water run over it. Make sure to dry it completely by dabbing it GENTLY with a SOFT cloth.
On the second to maybe 4th/5th day: Apply bepanthen 2-4 times a day to the tattoo (be careful not to use too much, your skin needs to soak it up). Keep doing the same as above in regards to water.
At this stage it shouldn't have gone scabby yet so you can apply the bepathen without too much worry.
Depending on how you skin heals and everything it will start going crust, it's CRUCIAL you don't scratch or pick at it at this stage! Even if it's the worst fucking most annoying itch you've ever felt don't scratch it. Running some luke/cold water over it should ease the itching a bit as well... Just DON'T scratch it ;)
Eventually the scab will fall off (1-2 weeks) - then you're in the clear.
If it doesn't look pretty you can now go shout at the tattoo artist ;)