riding mower and not damaging lawn

Hello,
I just bought a lawn tractor and have never even driven one before.
So this is probably a silly question, but do I need to do anything special to keep my lawn healthy when mowing it?
The property had been vacant for some time, so neighborhood kids had been riding their ATVs around our backyard, tearing up the lawn pretty badly in some spots.
I would like to reduce further damage while I work to get the lawn healthy again.

I was thinking along the lines of:

• mowing length-wise one week, alternating to go width-wise the next week
• does time of day matter for preventing damage? (morning dew, sun intensity,etc.)
• I saw someone mention making a Y-turn. So when i turn at the end of a row I mowed, should I do a Y turn instead of a U?

Thanks for any tips or advice!