Your character can stand inside the foliage near your own towers or allies to become concealed. Hide and wait for your enemy to become aggressive, then ambush them.
Control
Instead of dragging in the direction you want to move to, tap on your destination. Although dragging seems easier tapping gives you better direct control over your character's position. It also allows the screen to remain visible longer.
Kiting
Prod your enemy with a single attack or skill, then retreat towards your tower. When they come into range, they will get damage from your tower.
Money
Land the killing blow on an enemy to earn a bounty. Avoid auto-attacking creatures in a lane when not actively trying to take down a tower. This will allow you to earn more, and avoid pushing into enemy territory before you are prepared.
Spells
Directed spells are gestured based. When activated, a spell's range will be indicated as a circle which can be dragged into position. Have those spell circles ready to save some time, while still using non-targeted spells.
Teleporting
Teleporting has no cost, and just requires time to complete. Use it when low on health or when items need to be purchased. Teleporting from your own base will also give you a speed bonus.
Towers
When you are pushing against a tower or standing under it, kill minions as quickly as possible without waiting for a killing blow. The idea is to create space for your armies to focus on the structures, as well as reducing incoming damage to them.
Ambushes...