What is the proper way to run Category 6 underground?
Cat6 is capable of very high speeds (by today's standards; hi 2021!), but only within a bunch of additional constraints over lower-speed cable. 

Especially difficult is terminating the cable. When you untwist enough to terminate, it's easy to expose yourself to interference. Some people buy long, pre-terminated Cat6 and pull that, instead of pulling bulk cable, for this very reason. You'll need larger conduit if you take this approach.

Another difficulty is strains during the pull. If you tug hard to get around a corner, you can damage the cable enough to stop top speeds from working. Limiting the number of elbows, wide sweeps, conduit bodies, larger conduit, and having someone push while you pull all help.

You may decide that you don't need 10G speeds. In that case, save the money and pull Cat5e. Since you're running conduit, it's easy to upgrade later if you change your mind. It's a good idea to leave a pull string, but if you forget, just suck a new one through with a shop vac.

If there is any EMF in the same trench, a shielded cable will help. Ground the shielding at both ends. 

If you are sure you need maximum speed, consider using fiber. You'd put a fiber-to-ethernet converter on each end. Very long runs and EMF are non-issues. Cost scales well with distance.

To make sure I've covered your questions:


Is there a specific kind of Category 6 cabling I should use? 


Solid conductors, since these cables will be immobile. (Stranded is for wires that move often, like from your laptop to the wall.

Shielded is good for protecting against EMF, especially for long runs or if there is a power cable in the same trench.

Gel-filled cable protects against water intrusion that could cause corrosion.

Direct Burial cable has a tough jacket that can tolerate abrasion underground. If you're in conduit this matters less, but you might choose it anyway.

UV-resistant jacket is important if your wire comes out of the PVC where sunlight can get.


Can I simply run the cable through PVC pipe for most of the way?


Yes, and this is a good idea. Schedule 40 gray is the normal choice around here.


I read that Category 6 needs special grounding?


I dunno about that. 


Is there any major benefit to running more than one cable through the same ditch or pipe?


You can run multiple low-voltage cables through the same conduit if you want, but don't put power cable in the same conduit as low-voltage. Use a large enough conduit that you can pull additional cables later.


Are there any pitfalls I may not be aware of?


Many, but I can't think of any more.

EDIT: Since power will be in the same trench, I recommend staking the conduits to their respective sides before filling, to make sure they keep a good foot space between them. I wish I had known to do that!

For future-proofing, consider installing an additional conduit. A contractor friend likes to install an extra 4" conduit, which can be used for a lot of stuff. Other people think he's nuts. I think they're both right. :-)