At the start you've basically got two monsters to train on and they are cows and chickens. You train on these until about 5-10 range (defense is optional if your starting an account).After level 10 go and attack goblins until level 25 range.
Then go to the wizards tower and attack spell wisps until level 40. If you do the tasks at the combat academy and put all the reward books onto range XP you can level you character up to 20 range and skip the cows/chickens).
We also recommend taking an inventory full of impious/accursed urns as the wisps drop impious ashes and the lessers drop accursed ashes so you can train your prayer at the same time. At level 40 Range go to the catablepons on the third level of the stronghold of security and train there until range 60.
At level 60 Range you can head off to karamja and go into the tunnels and kill the lesser demons there. If you are a low defense level there are a couple of safe spots to shoot from. It is recommended to collect your arrows as it save a fair amount of money. If you have 25 dungeoneering you have access to the resource dungeon where it should be less crowded. Just train on lesser demons until level 99 range or whatever your target level is.
Obviously you should use the best short bow and armor you can get and use iron arrows until you fight the lesser demons, and then you can use steel or adamant arrows. When training take a shield bow with you to rejuvenate, or take some food).
From 70 Ranged to 99, you can also try killing the Giant Spiders in Stronghold of Security. Hope this guide is useful to Range rookies.