TTR tests are performed through primary injection . Number of turns are changed through tap changer, and the effect is measured on the output side to determine if the secondary voltage correspond to the primary injection at a particular tap.
Transformer turns ratio can be done in a number of ways. You can do voltage like what was mentioned before, or you can back calculate based on relative inductance/impedance/etc.
The optimal way to test for turns will vary based on the size and type of transformer you are testing.
Further complications will happen if the transformer uses a 'gapped' structure to keep it from saturating. This will throw off the inductance style of turns calculations.
When testing with voltage, you must also be sure to stay well below the saturation level of the transformer (Bsat) or you readings will be off as well.
Voltech and Wayne Kerr both have some good info available on this if you do a web search for them. I would try Wayne Kerr first since their customer service tends to be better.