Start by placing the "starter brick stitch" on your middle finger.

Take the longer strand that points towards you and bring it UP, OVER and ACROSS the starter stitch to form the first loop. Use your pointer finger to hold this loop between it and your middle finger, as shown...

The other long end, the one facing away from you, should then be brought UP, OVER and ACROSS the starter stitch to sit next to the first loop to form your second loop. Use your pinky finger to hold this loop against your ring finger...

Take one of the inner strands UP and OVER its nearest loop, then ACROSS and UNDER the second loop...

...and let that short strand hang off your hand. Note how the second yellow loop, the one on the right, holds the pink strand in place. If you had started with the other pink strand, you'd note that it would fall out of the loops, which is NOT what you want to do! :-)

Alright, now grab the other short strand of the same color and bring it UP and OVER the nearest loop, then ACROSS and UNDER the far loop...

...and let this strand flop off your hand as well. In this shot, note the possible problem we might have if we're not careful. Can you see it? Look closely at the last pink strand we were working with...

Continuing, grab the next short strand, on the opposite side, and bring it UP and OVER the first, then ACROSS and UNDER the second loop. (Are you still looking at the second pink strand? The problem is still there...)

Pull this strand through fully. Note how I corrected the problem with the pink strand from earlier? Did you catch what the problem WAS? That strand was TWISTED and would have caused the finished stitch to have an odd appearance when you compared it to all the other stitches.

Finish your last short strand now: UP and OVER the first loop, then ACROSS and UNDER the second loop...

...and pull it through. We're ready to start pulling this stitch together!

I zoomed out quite a bit for this shot. Note, specifically, the placement of my fingers. This is that 4-way pulling I was talking about earlier. I use my thumbs and pointer fingers to pull away from each other in one direction, while at the same time using the remaining fingers and the cup of my palms to pull away from each other in the opposite direction.

Zoomed in a bit more and you can see how a finished twist stitch looks almost identical to a brick stitch.

Here's what the stitching looks like after a bit of work...

...and here's the ever popular "bullseye" view, ready for one last stitch.

A Twist Stitch Project, properly completed!