Chrissie, to find mithral, or any mineral or gem stones, you must mine for them. Set your blacksmith at a pile of rock, select "discover", then select "collect". Once discovered the pile of rocks will have a tag telling you what it is.
Mithral can be discovered to the left side and toward the rear of the Peteran church, (or where it will be if you don't have it). There are two piles of rock there and one is mithral. The beach is also an easy source. Your smith will use a lot of different things so mining a lot is a good idea.