Yes, drain from the bottom.
As for refilling, if you have an ATF dipstick, they will pour the fresh ATF into your dipstick opening via a funnel adapter. For those gearbox that don't have an ATF dipstick, they will pump in from the bottom of the car via a refill opening, the refilling lug located about 1cm above the gearbox sump.
Few things that's part of the procedure, like warming up the gearbox to 50 degree Celsius before draining, after refill, need to start the engine and move the gear shifter through all level to circulate the ATF for few minutes, then check level again, etc.. workshop mostly work "smart", if they never see your face before, very likely they will take short cuts.. especially went u not watching. For that reason, I'm not recommending any workshop because you may not get the same service level even though same workshop. For me, I don't trust any workshop.
Good luck!