Assuming you don't get delayed, it should normally take you three turns to get in and through a gate to seal it.
Turn one: enter and Other World encounter
Turn two: move forward into second area of Other World, have another encounter
Turn three: move out and seal or close the gate.
Avi, for all his corruption, is spot on. Important note in Arkham is to pay attention to the phases.
Heavily unrelated note:
Me and Brian came across with a freaky way to open a gate yourself and seal it during 1 turn. You need Naacaal Key from Black Goat expansion, Find Gate and Erich Weiss ally or Mark Harrigan (or some other way to prevent getting delayed).
Naacaal Key requires movement points and if successful, opens a gate of your choice at your location (side note, good for vs Atlach, open and seal a gate at a stable location , of course not really sure you can do that ). I originally felt that you'd only get sucked in during the encounter phase, but ColtsFan76 was of the POV that it'd be like getting "a gate appears" encounter and thus delayed. From there, I was off. Since you enter the gate already during the movement phase and being Mark (or having Erich) prevents you from being delayed, you can then cast Find Gate and return to Arkham, ready to close/seal during your Arkham encounter.