Dr. Hewett is correct, horizontal. Though whenever I ship cells or move cells from lab to lab I always fill the whole flask with media and then paraffin the cap to prevent leaks. This way there is no risk that the cells might dry out (which is the primary risk in moving cells) and also the diffused CO2 in the media make sure the cells are in their optimal conditions during transport. When the cells reach their destination uncap them, put them in an incubator and give them a few hours to allow floaters to resettle.
To add to Dr. Adams answer- if you are all capped as he points out, you shouldn't lose too much C02 and your pH should be fine. You also can add HEPES to the medium (10 mM) to be extra careful. At the point of destination, you can put back into your regular medium after those floaters resettle.
I would transfer them on the flask (when you see they are happy and proliferating) with the para film as other researchers said, be sure you pack it in a sealed box so nothing comes into the flask, to be extra careful.
Ideal thing would be to freeze down your cells and transfer them in dry ice, but I assume this is not convenient for you as you are just changing laboratories for a short period of time.