The sump pump I want to use for a utility sink install I want to do myself is a Liberty 404. The sink is going in my basement and all the drain pipes are on the ceiling of the basement. I am new to plumbing and Im confused about the vent output on the sump. I know that houses use vent pipes in the drainage plumbing that usually go out the roof. Im just not sure how I need to plumb the vent output on the unit to my existing plumbing. Any help will be appreciated.

the discharge from the pump can tie into an available drain but must not tie inbetween a fixture and its vent.
get us a picture if you are unsure of the tie in point.
as for the vent..
the discharge has a check valve in it so you don't worry about sewer gas coming back so any odors that might come back from the tank vent will only be from the tank itself. a short pipe out of the vent opening on the tank with a double 90 on top (candy cane) will work.
do not use an AAV for the tank vent.
of course if you wanted to bring the tank vent up and tie into a proper vent stack, that is ideal.

Thanks for the reply. I just took a short video to show everyone where the sink is going and where the plumbing is. Heres a link to it:

[www.youtube.com]