The tetrazolium test is an alternative viability test based on the assumption that living tissues will turn red-pink when soaked in a solution of triphenyl tetrazolium chloride. You can use seeds that are freshly collected, have been stored, or are at the end of a germination test. In the latter case, you just use the seeds that haven’t germinated.
The test has the advantages of being relatively quick (a few days) and of giving some information on species that are slow or difficult to germinate, but it can be time consuming and require trained operators to perform the test correctly. A tetrazolium test is not an absolute test of seed viability — the protocol changes slightly between species (with guidelines not available for all wild species), and the interpretation of the results can vary significantly between operators. Basically, the more experience you get with the test, the more confident you will be in relying on its results. Finally, you need to perform the test in a lab, with some lab equipment, and you need to consider the additional cost of the tetrazolium solution.
You can find detailed instructions in the Manual of Seed Handling in Genebanks, and specific protocols for several species in the AOSA Tetrazolium Testing Handbook and in the ISTA Working Sheets on Tetrazolium Testing, Volume I & II.