This guide is meant for the Summoner's Rift map.

In the beginning of the game, keep your distance from enemies, using Q solely for attack (so build on it first), either hide in a brush with a warding totem or stay under a turret and farm on minions.

When you get enough gold, start buying items meant for damage and health (cooldown reduction as third if you have enough slots and gold). When your health is strong enough, gradually attack closer to enemies but don't spam attacks at them yet, until you've unlocked R.

Once you do, go all-out with your attacks and you can easily get multiple kills. Gnar can be small but when he's in mega Gnar form, he can be very much overpowered with the right damage+health items.

If you don't have enough gold, put emphasis on health as Gnar tends to die easily, and maybe get an armour. I managed to achieve 16 kills in a game against bots, but at the same time my Gnar died 16 times also. So he has good potential in getting kills, but you've to take care to make sure he doesn't die so much. If you have unlocked flash, use it in place of heal to escape from enemies.