Start at the middle camp closest to your side, if you get wraiths try not to use smite in case you get golems at the next camp. Some teams leash the first camp, others just contribute damage. Then run to the top right or top left of the map to that camp depending on what side you are on.
Use smite on the golems or as needed and later in the game make sure you save it for important buffs like red and dragon. So timing buffs is also your job.
If they don't have a jungler you can then go to the top opposite camp of your top camp and take that as well. Wriggles is important, but not all need it.
People without mana are really strong like shyvana and riven. But people who can hop walls like jax and lee sin are unreal. I've also had success jungling malphite and naut and recently I was able to clear successfully as Alistar. Udyr is also good.
If I am unclear feel free to add me and I could show you in a custom game or something, or if you even wanted to scrim.