How to determine which wire is which on a transformer?

In a step-down transformer, the primary winding will have a higher resistance. The resistance will be low, but there should be a noticable difference unless you've got a really big transformer.

If you're trying to identify what a winding is, then here are some notes:

• If 3 wires have continuity, then you probably have a center-tap winding (+, 0, -)
• If only 2 wires have continuity, then that is a simple winding.
• If 4 or more wires have continuity, then you have a multi-tap transformer winding.

Transformer windings have a phase relationship, but it's typically not important for power supplies. Unless one of the wires has continuity to the transformer core, the polarity doesn't matter.

A relatively safe way to test transformers is to hook up a small AC voltage (1-5VAC) and measure the voltages across the other windings.

The primary's wire is thinner and as W5VO says has a higher resistance. For the secondaries I presume they're separated. To find start and end of a winding you measure resistance with your multimeter. Depending on the transformer's rating you'll measure a few hundred ohms between begin and end of a winding. If you measure mega-ohms your measuring on two isolated windings. Let's say you can find windings A-B, C-D and E-F this way. To find the polarity you'll have the connect the primary to the mains. Measure the AC voltages of A-B, C-D and E-F. Let's say these are 19V, 19V and 12V. Those are unloaded voltages, and especially for toroidal transformers those may be much higher than the rated voltage. In my example rated voltages might be 2 x 12V and 8V.
Now connect A to C and measure the voltage between B and D. If this is 0V (very low anyway) A-B and C-D are in phase, so if A is the "start" of A-B, then C is the "start" of C-D. If the voltages are equal you can place them in parallel to double the current.
If the voltage measured between B and D was 38V the windings are in anti-phase: if A is the start of A-B then C is the end of C-D. You can connect the windings this way to double the voltage or swap C and D to have the windings in phase again.

You can do something similar with the third winding. Connect A to E and measure between B and F. If the voltage is higher than 19V (still working with my example) then you have connected the start of one winding to the end of the other. If the measured voltage is the difference of the two windings' voltages then you have connected start with start. You can use either way of connecting to create higher or lower voltages.