I did this last fall, and will share my experience, though I can't promise it hasn't changed.
When you reach the immigration area at Dubai's T3, there is a separate line for Smart Gate registration. The process is essentially the same as any immigration control: hand over your passport, answer any questions the officer might have about your trip, wait a moment while they scan your passport and check the computer. You'll then be asked to look straight ahead while a camera captures your biometrics. The officer will tap a few more keys on their keyboard, and you're all enrolled. The registration process is described as taking "around 20 seconds." Once you're done, you just walk past the counter to the hand baggage x-ray required for all arrivals in Dubai, then to the baggage claim.
In short, it's just the normal immigration process, with a brief additional biometric scan added.
Note that, when I was there, the Smart Gate registration counters had a line, while the normal immigration counters did not. I ended up wasting a bunch of time registering for a time-saving service I am unlikely to get much use out of, but your mileage may vary.