Learning not to chase players into their towers is a great first lesson. I think the biggest lesson to learn is lane control. Own your lane and stay in it. Kill creeps and cap flags until you've got a level advantage then still only press your luck when you have the numbers advantage. Stay aware of what your teammates are doing, if they're running and you're nearby you may be able to peel off their pursuer and save your team a death.
One of the hardest lessons to learn is how to not take damage in the early game. If you're repeatedly running back to the crystal you're not xping or making money and your teammates are fighting shorthanded. You're better off sitting next to your tower and killing the creeps as they come up than charging out to the flag to fight a 50/50 battle that you may have to run from and leave the tower open.
Capitalizing on the money you make is pretty key too... you're going to need how to learn how to use TP scrolls, cap locks, and sigils so I generally don't buy any items past the 2nd level... unbreakable boots, plenor, vlemish, hauberk of life, nimoth. Sometimes a narmoth's ring or mageslayer depending on the circumstances of the game. I don't ever specifically look to upgrade my weapon dmg or attack speed, I'd rather have maxed out cats and giants doing the dirty work at that point. Mana is highly DG dependent... I play UB and Oak. With UB I'll grab a vlemish and be fine, with Oak usually I'll get both a vlemish and plenor if the game lasts long enough. Some other DGs you might need a 3rd mana item depending on your build. But if you're not sure, it's hard to go wrong by stacking HP.
