Thanks to Beast for the original Torva repair guide. It was useful to me but left out some details (for me at least, since I'm a total noob), so this is intended to help anyone who got stuck along the way like I did.
You can see Beast's original guide here.
Step one: Bandosian components are required to fix the damaged Torva. You must dismantle Bandos armour pieces to obtain these. Dismantling Bandos chest plates give you three pieces each, and tassets give you two pieces each. In total, you need four Bandosian components (1 x each for the Torva helm and legs and 2 x for the plate body).
Step two: The Ancient Forge is required to dismantle the pieces—it can be found in the Nex boss area. Teleport to Nex using the teleportation tree at Edgeville. To enter the room, you must have 70 agility. You can train this at Tree Gnome Village to level 52 and then the Wilderness Agility Course to level 70. Once you've gained access, go to the forge icon on the mini-map and use the Bandos armour pieces on the furnace to get the Bandosian components.
Step three: Finally, you will need to use the Bandosian components on the broken Torva pieces with a hammer in your inventory AND 90 smithing.
And boom!
After grinding out 90 smithing, you now have some shiny new Torva pieces in your inventory.
Cheers!