What is an effective way to level smithing?

Value Matters now. It used to take about 400 iron daggers to level up to 100. Now it takes about 2400 iron daggers.

From UESP: http://www.uesp.net/wiki/Skyrim:Leveling

• 25 + (3 * [item value]^0.65) base XP for constructing an item.
• 25 + (8 * [item value delta]^0.6) base XP for improving an item.

So, making more expensive things and adding more value is a good thing. But making something twice as expensive does not give you twice as much experience.

Early Stage

First, try to stack as many XP boosts as possible. Make sure you activate the Warrior's Stone for a 20% XP boost, and get a good night's sleep for a 5% - 15% XP boost. If you're further along in the game, completing a certain quest will add another 15% bonus to your Smithing XP gain.

Making iron daggers and leather bracers is still good way of leveling up in early stages. It's quite useful when your level is low.

Jewelry is another good way to level up in early stages. You can obtain large amounts of gold and silver ingots by buying or mining iron ores, which are cheap and plentiful, and turn them into silver and gold ores with the Transmute Mineral Ore spell. Don't sell the gemstones you get from mining and adventuring; use them to craft even more valuable jewelry.

Training is very inexpensive under Level 50, especially if you sell off all that jewelry you're crafting.

Mid Level

Dwarven Smithing (Level 30): Useful if you're going up the right side of the tree. Dwarven ingots are plentiful in this game. You can get scrap metals from Dwemer ruins and turn them into dwarven ingots. If you have Dwarven perk on the right side of the Smithing tree, you can take advantage of this. Once you reach Level 30 in Smithing, you can start making Dwarven Bows (2 dwarven ingots + 1 iron ingot) and upgrade (1 dwarven ingot).

Advanced Armors (Level 50): Useful if you are going up the left side of the tree. With this perk, you can start making Steel Plate Armor. It has the highest value added ratio, so very likely you will make profit even if you buy Steel and Corundum ingots, make Steel Plate Armor, upgrade it, and sell it back to the blacksmith. Speech skill and being able to get good deals is somewhat important for this strategy.

High Level

Upgrading an expensive armor adds a lot of value as your level gets high in smithing. You increase the value by 50% for upgrading to Exquisite (Level 40 with perk). You double the value if you upgrade the armor to legendary. This effect is amplified if you use Fortify Smithing enchanted gear and have Fortify Smithing potions.

One way you can take advantage of your high smithing level is to buy expensive armors and weapons at the blacksmith, upgrading them, and selling them back. If you have items that enhance prices (Volsung, Masque of Clavicus, Necklace of Haggling, Potion of Fortify Barter), you can make profit doing this.

Outdated:

To quickly level smithing, you should primarily focus on leather bracers and iron daggers, due to the fact these are two of the cheapest items to smith, and can be sold to cover any expenses.

The materials required, iron and leather, are fairly cheap and are easy to find. If you have a nice lump of cash, it is more effective to use this method and ignore making armor for your level. The reason for this is that you will be quickly leveling, allowing for constant improvement, as well as an increase in the effectiveness in upgrades (ranging from Fine to Legendary).

New:

In the recent patches of Skyrim, it is more efficient to focus on more expensive equipment to level smithing. While it may not cheap, crafting higher level equipment is definitely more cost efficient. While I'm unsure of the exact values, try finding a balance between mining trips and buying ores in order to keep up with smithing production.

I'm currently level 100 smithing, I found that doing steel daggers, iron daggers, and leather bracers the most effective way. Also, buy and smith in whiterun, fast travel to riverwood then buy and smith there, then go back to whiterun, wait ~48 hours, rinse and repeat.