I just did my first E6 yesterday, using a Paterson Chrome 6 kit and Fuji Velvia. I did it using an ordinary stainless steel manual tank. The worst of it was getting the temperature right -- I just had one of those days when I kept mis-reading the thermometers, so I was constantly messing with the water in my water bath. I finally got it right, though, and the results are fine. It was pretty weird seeing positive images come off the reel on which I normally see negatives, though!
As Mick says, the stabilizer is the final step. It's basically a combination of Photo Flow (or something like it) and formaldehyde, the latter being necessary for long-term archival stability of the images. The general advice, as Mick says, is to keep stabilizer out of tanks and reels; however, I believe that's mostly a factor for plastic tanks and reels, because the stuff tends to gum up the reels. I've had no problems with C41 stabilizer with my stainless steel reels (but I've done only about a dozen color rolls so far). I don't know offhand if C41 and E6 stabilizer are interchangeable, but I believe all the same caveats apply to both of them.
My main advice is simply to read, re-read, and carefully follow the directions with your kit. Assuming your Tetanal kit is like my Paterson one, the number of steps (chemical baths and washes) is greater than with most B&W processes, so it's easier to get lost. Of course, if you're using an automated machine, it's more a matter of being sure it's programmed correctly than of following the steps yourself.