Steel Golems are a variant of the war Golems that the Dwarves used to create. These are made entirely of steel and are presumably stronger than their Stone Golem counterparts. By the current age, they have all but vanished from existence - excluding some that the Warden meets, there may be more somewhere.
As Steel Golems are all but wiped out except for the Paragon Caridin, all involvement for Steel Golems centre around him which makes it a rather big part for the most of it. Caridin will be the one to help Shale remember some of her past as well as being the one to side with if you wish the Anvil of the Void to be destroyed.
Outside of Caridin two more Steel Golems exist in the first game, and can be found near the end-game during the "robbery" quests, they will be automatically hostile to you. And while they are weaker than Caridin is in a fight (due to the fact Caridin is a boss while these two are Lieutenants) they still carry the same attacks and can be rather annoying if they decide to fire off the lightning DOT/AOE that Steel Golems have.
If the Warden chooses to help Branka and saves the Anvil of the Void, four steel golems will be available as allies against the darkspawn in The Final Battle . They are counted as their own army but do not have their own emissary in the party camp, and as such resources cannot be donated to them. They are, however, perhaps the best army in the game in terms of damage and durability, and it is possible to overcome the entire siege of Denerim utilizing only they and withstanding only a single casualty.
In the Dragon Age - Awakening expansion, three Steel Golems can be encountered at Hirol's Shrine, and two more at the Shrine of Korth. A heavily modified and dangerous Steel Golem, known as the Inferno Golem, appears at the Kal'Hirol - Lower Reaches. The Golems in Hirol's Shrine will remain inert unless the player disturbs the sarcophagus, resulting in their hostile awakening. In the Shrine of Korth, they will only attack if the player steals from the altar.
When encountering the last two Steel Golems of Origins, which are part of the Slim Couldry line of quests, the easiest way to deal with them is, well, not to. The golems are triggered by pressure plates within the room, spread out in a checkerboard pattern of five. Disable all five (which requires a rogue with the appropriate skill) and the golems do not activate - allowing the Warden to enter the vault and retrieve the Tears of Andraste untouched.
If you do desire to destroy the golems, note that they behave precisely as Stone Golems do, just with increased stats. They have greater armor, health, and damage, and triggering the traps also fills the room with poison gas, dealing damage to all companions.
The most experience is gained from disarming four of the traps, then activating the fifth and killing the two golems. The traps are all deactivated (and cannot be disarmed) if even one is activated.