See Pussy
Especially for anal fisting, you'll want to make sure the entire area is cleaned out prior to your session. As the giver, it's a very good idea to wear latex or other protective gloves. For anal fisting, it's mandatory. Proper hygiene is the key to having repeat sessions that are both exciting and enjoyable. As the receiver, you don't want to be walking around funny for the next week (or maybe you do).

Start Slow
Make sure to start each session with a little warm-up before trying to cram your whole arm up there. As you get more experienced with fisting, you'll get to know your partner's preferences and thresholds. It's easy to get caught up in the moment and just ram that fist up there, but you're better off with a slower, probing approach. You'll know when they want you to go full tilt.

Lots of Lubricant
It's almost impossible to use enough lubricant. Also, you'll want to liberally apply additional lubricant as your session wares on. Oil based lubes work wonderfully, but if you're anal fisting, you may wish to consider a water based lube. Make sure to lube the fist, the wrist and the entire opening, including the inner walls.

Relax
If you're the receiver, make sure to relax your opening so the giver can work their entire hand in. You'll be amazed how much you'll stretch and how comfortable it will become once the whole hand is inside. Let your mind and body relax and breath outward as you go through the peak insertion stages. You'll find that the opening will loosen up and allow for the sublime pleasure of being stretched to the limit.