There are many ways (sorted starting with easiest):
- If you know the part number - Google it
- You do not know the part number, but the package is standard (TO-220 for example) - you can find legs specifications in package's spec (or just find a datasheet of any other similar transistor in this kind of package). Some standard packages are symmetric though :(
- Diode mode measurement (as seen in the video)
- Resistance mode measurement (instead of measuring diodes' forward voltage, you measure the resistance between pins)
- If none of the above worked (or you just don't have a multimeter) - you're dead in the waters
EDIT: while it is nice as a theoretical example, in practice you will never work with an unknown component (unless you're really desperate), therefore you'll always have datasheet.