Chuck, a 40-circuit (or 42 for 3-phase) panel is designed to reject tandem breakers, because that would exceed the lawful limit. Therefore, you need two sub-panels; one near the main panel, (for the space) and one for the HT; a 125-amp rating is typical. Neither sub-panel needs its own main breaker.
The best bet here is to install a small panel, perhaps 6 or 8 spaces (for future use, too), next to the main panel, and move two 2-pole (move the lowest-rated circuits) or four 1-pole breakers (and circuits) to the new sub-panel. This will give you the space in the main panel for both sub-panels' breakers.
You'll need a 2-pole breaker to feed each sub-panel; the proper rating depends on the wire feeding each one, and that depends on the load expected. For four to six 15- or 20-amp 1-pole breakers, a 30-amp 2-pole is plenty, and a #10 feeder is good. For more, go to 50 amps and a #6 feeder.
In each sub-panel, the grounding (bare) wires and neutral (white) wires must be kept separate. This means that the neutral strip remains insulated from the enclosure, and a second strip gets screwed to the enclosure for the grounds; therefore, the feeders should be 3 conductors (plus ground).
As for who should do this work, the fact that you asked (no insult intended) implies that you should hire a licensed electrician. It's not terribly complicated work, but errors can have dire consequences. If you're extremely handy, and can acquire proper material, you might do it yourself. IN that case, have it inspected!
(Okay, so Impeyr types faster!

)