We've camped with our daughter since she was 3 months old... Cheap vacation!
The Baby Bjorn we found especially useful, since we could do camp activities with her right there, and she loved being a part of the action. We usually had her facing out, but when she'd get sleepy, we'd face her in. As she got bigger, I splurged and bought a baby carrier/backpack from a thrift store for $5. She'd ride in it when I did yard work, so having her in it at camp wasn't a big change.
As for sleeping, she'd fall asleep in her carseat. Otherwise, we had a bassinet from an old-fashioned baby carriage that we'd lay her in, and it'd only take up a corner of the tent. I've seen people make a round bed with blankets and an innertube.
First solid food was a burnt hot dog...