A zero sequence set of voltages are all in phase. This characteristic means that you can perform a test with a single phase source and simply jumper the source-side terminals together. The load side terminals would be shorted together.
Analytically you can see what impact a particular winding connection will present. For example, if the source winding is delta, if you apply a single phase source to a delta and jumper all the phases together, you have effectively shorted out each delta winding so no current can pass through this winding to the secondary.
If the source winding is a wye or star, then you can apply a single phase source to this connection. By jumpering from phase to phase, you will energize each winding with the same source voltage and you will get current flow to the secondary.
You can look at the T&D Book, Wagner & Evans, Grainger & Stephenson or Charles Gross and others and find the equivalent circuit for a variety of two and three winding transformers. Once you reflect on doing the test with a single phase source, it should make more sense to you.