Crosswise....
With your feet and head hanging off?
Hahahaha... no.
OK, if you've got one of the hammocks that have the cross-bars at the end, you'll lie in that 'normally.' But, since hammocks didn't originate in the US... we use them wrong. Also, this doesn't count with the "military" hammocks that have mosquito nets, bells, & whistles.
The ends tie to the tree, or whatever. You lie perpendicular to the ends. Sit your butt down in the middle of the hammock like you normally would, then put your feet into the edge (so you're in a fetal position). Don't swing 90 degrees and put your feet towards the ends that are tied. Once your feet are on the edge, kick your feet out, then stretch out your torso. It takes a second to figure this out, but the hammock is A LOT more stable this way. You can also sit with this method, by adjusting where you put your rear-end initially.
http://www.fungifts.com.au/images/products/small/hammock_320.jpg