Our popup had an adapter with barbs on it that you can put a piece of clear tubing or garden hose onto and then run that away from the camper to a holding container or bucket. You can get them at camping supply places too. I just bought a second one, as I have a short piece of hose for a bucket, and now a longer one for sites where I have sewer hookup to connect my grey water to.
What I found out though was that our sink has a trap, but no vent. So just like F1100turbo posted in his pic above, I am doing the same. My out put is 1 1/2" diameter and I have a PVC Tee connected to that. On the top, you see his black piece, that is an Air Admittance Valve, available at Lowes or Home Depot. This will allow air into the system to vent your drain line and allow water to flow easier, without letting the grey water odors back thru the vent. This is also nice to have if you are at a site with sewer hookup that you are going to drain your grey water into.
2008 Toyota Sienna LE w/ Airlift Airbags
2012 Flagstaff 208 MAC Tent Camper