You'll need a stable secondary resistance of known value, and you'll have to monitor voltage across it throughout the test. If you want to measure current, you can use an "unknown" resistance - as long as it is stable. You have a choice, and you can make your calculations based on either one.
Your equipment will have to be "accurate" at least to the degree of accuracy you wish in your results.
Hook up your resistance to the secondary, hook your equipment up to the various places you'll need it to make your measurements, plug in the primary and flip the switch. Observe and record.
Your data will allow you to make calculations. Primary voltage times primary current equals primary power (power into the primary). Secondary voltage times secondary current will equal secondary power (power out of the secondary). There wil be a bit more power "put into" the primary than is "taken out of" the secondary because of losses within the transformer. (These will be resistive losses in the wire as well as inductive losses in the core - eddy currents.) And that is what efficiency speaks to. Transformer efficiency can be calculated using the following formula:
Efficiencytransformer in % = 100 x (Powersecondary / Powerprimary)
If you opt to use secondary voltage and the resistance of the resistive load to make your calculations for the secondary side power, it will be found by using this formula:
Powersecondary = (Voltagesecondary)2 / Resistanceload
Either path should lead to the same destination. And just so you know, if you use secondary current and the resistance of the load to make the calculation, that is done using this formula:
Powersecondary = (Currentsecondary)2 x Resistanceload
All roads lead to Rome.