How do you smelt ore?

I've gathered metal ore from a mine, but the forge only uses iron bars to create items. I can't seem to find an option to convert my ore into bars; do I need a special kind of forge, or I am missing something obvious?

What you are looking for is a furnace/smelter, which is typically in the shape of a very large, cone-shaped oven. Not all forges have a smelter, but Whiterun has one.

A list of all smelters can be found on this site

In addition to Wimpey's Answer, there is another smelter out in the field by Soljund's Sinkhole.

Much less accessible than the one in Whiterun, but this is just saying that another one is available.