Fleching
Buy or chop regular logs (Catherby is a good area to obtain logs), make shafts, then longbows. Switch to willows when you can.
Herblore
Druids drop a lot of herbs, so head to the resource dungeon under Edgeville or the dungeon under Yanille to gather some.
Agility
Start at the Burthorpe and Gnome Stronghold agility courses. Finding the circus will get you some easy experience.
Thieving
Pompous Merchants in Burthorpe until level 5, then cake stalls in Ardougne.
Slayer
Go to the best slayer master available to you.
Farming
Get some potato, onion, and cabbage seeds. Start planting in allotments south of Falador, north of Ardougne, North of Catherby and east of Canifis. Check back every so often, don't just stand there waiting for crops to grow. Start oak trees as soon as you hit level 15.
Hunter
Head to the Feldip hunter area (south of Yanille) and catch some crimson swifts using bird snares, or head to Burthorpe or the snowy hunter area (North of Camelot) and catch some polar kebbits with a noose wand.
Construction
Buy some planks or chop logs and turn them into planks at the sawmill north east of Varrock. Also buy some nails, just for the first few levels. Higher level nails break less often. Head to any estate agent and purchase a house. Start building things.
Summoning
Gather charms from training slayer. Complete Wolf Whistle quest to learn how to use them.