To begin, all you need is with is level 10 Mining, so the requirements are low , and RS gold this quest is definitely faster than the regular methods of training. In addition, if you're already an experienced player and are at level 20 in Magic and level 20 in Mining, and level 20 in Crafting you can also complete both parts of Elemental Workshop quest.
This will take you straight to level 35 without having to worry about other Smithing levels methods. If you'd like to keep exploring later, you can complete the Giant Dwarf quest which later will be required for the other methods. There are additional Recipe for Disaster, Devious Minds, Cabin Fever, Elemental Workshop II, Family Crest, Fremennik Trials which you can complete to have the best experience. Keep in mind that all of these quests are for members so f2p players can't complete them. Unfortunately, neither the free to play quests reward players with Smithing experience.
LEVELS 29-40 IRON Items. In this bracket, you'll need to make the best possible iron products from iron bar you can make - similar to Iron Platebodies. Leveling up to 40 should take around an hour with about 1000 bars of input. As mentioned before the best location to start is at the western Varrock and cheap OSRS gold you can begin making your pieces of Armour there.