My camera has a setting specifically for them. It shows a bit of your last photo down one side and you line up the next one to match.
It also locks the exposure to the first photo so if you're doing a full 360 it's worth lining up the first one and doing the half-depressed button bit to autofocus then holding the button there and spinning round. Sometimes you'll find the trees or hills are too dark or the brighter areas are washed out when you get to them. If so choose a slightly lighter or darker view as your first image and try it again.
You can take them with cameras that don't have an assist function too, it just takes a little more mental discipline.
Use manual mode so your exposure is locked as mentioned.
Other tips:
Turn on gridlines or a bounding box(if your camera will let you) to help you stay level, the wonkier the assorted horizons are the more you have to crop off the top and bottom of the finished picture.
Wonky horizons make things harder in the stitching software too, they induce waves that are a pain to sort, you're sometimes best taking [a copy of] the images through photoshop and rotating/cropping/saving them first to get them level.
My current camera is set to 50% overlap, my last was locked at 20%. It means 12 pics per rotation instead of 8 but I reckon it's worth it for the ease of leveling the images. I also have two 360s which are missing a few degrees because the canoe was rocking and one bit of forested hilltop can look surprisingly like the next sometimes. I doubt that would have happened if the overlap had been higher.
Stiching software enjoys woods a lot more than lakes.
PTGui walks all over any of the free stitching software(and any of the
Pro versions I tried as well). Switching to it was like an electronic breath of fresh air.
If you're trying it and get into any bother feel free to give me a shout.