You could easily be forgiven for thinking that a rock is just a rock, and that it doesn't really matter what kind of rock you put in your sauna oven. However, this is not true and one of the most debated questions of applied geology1 in Finland is the one about the best rock types for sauna ovens. Ideal rocks should have good resistance towards chemical and thermal weathering, a high heat capacity and should not contain harmful minerals.
It is far easier to determine rocks that should not be used than to actually name the best choice. First of all, you should make sure that the rocks you are going to use don't contain sulphur minerals such as pyrite, pyrhotite, arsenopyrite or galena. If you're not a geologist and don't recognise minerals, avoid those rocks that have minerals with a yellowish colour and/or metallic lustre. Sulphur minerals weather easily and release sulphur into the air. This is not a real health risk, but means that you'll have to replace the weathered stones sometime soon.
Another unwanted mineral group is asbestos minerals. If you can't make a distinction between asbestos and other fibrous minerals, just dump all rocks with fibrous minerals. The reason for this is that when you throw water on the asbestos-bearing rocks, small amounts of it are released into the steam and parts of it end up in your lungs. Asbestos is proven to cause lung cancer, and although the probability of getting it by having a sauna is naturally small, it exists.
Sedimentary rocks in general are bad choices - their structure is normally far too weak to stay intact when heated and cooled successively. Metamorphosed sedimentary rocks are not much better either; schistosity2 and other directional structures limit their lifespan as oven stones. This is caused by different expansion coefficients in different directions. Quartzite with strong orientation heated in the oven can actually 'explode'3 when water is thrown on them.
With the limitations mentioned above, you are left with not much more than the large family of unaligned igneous rocks - and preferably dark-coloured igneous rocks4. Dark minerals5 are good because they contain magnesium and iron and therefore have a relatively high heat capacity, meaning that they can store more heat than other minerals, which in turn makes for a good sauna oven rock. Other reasonable options are highly metamorphosed volcanic rocks that have not developed too strong an orientation6.
Size and Shape Matters
For normal continuously-heated ovens, the best size is about the size of a fist. Bigger ones take too long to warm up and smaller ones give the heat up too fast. In 'once-heated' ovens, the right size is about the size of a volleyball. The ideal shape is approximately equi-dimensional, and best of all are smooth stones from rivers or seashores. If you buy the stones from a hardware store, you'll probably get crushed stones that are neither very smooth or equi-dimensional, but don't worry - they'll work just fine.
Placing the Rocks in the Oven
Before putting the rocks in, be sure to rinse off possible dust, etc. Don't try to pack the rocks too tight, because this prevents the air from circulating and slows the heating of the sauna. Pack the rocks as loose as you can, as long as there isn't any danger of the structure collapsing.
If you have an electric oven, you should have enough stones to cover the heating elements. With wood ovens, you should have enough stones to form a small mound rising above the rim of the oven. Approximate amounts of stones are normally provided in the installation instructions of sauna ovens.
Replacing the Rocks
Yes, it doesn't matter how good the stones are that you've found, you'll have to replace them some day. Timing depends naturally on the quality of the stones, the amount of use and the type of oven. But when stones clearly change colour and start to turn into sand, it is time to change at least the most weathered ones.