Here is what the pattern says:
Dividing round: K 20 sts, leave on needles for back of hand; bind off next 22 sts in ribbing. Fasten off.
Underlap: First Stripe: With C, cast on 22 sts, k 1 row, p 1 row for 4 rows. Break off. Work 3 more stripes, 1 each of B, A and C. Break off.
Joining round: With B, k 20 sts of back of hand, join and k 22 sts of underlap; 42 sts. K 3 more rounds with B, break off B. With A, k 4 rounds. With C, k 4 rounds. Break off C. With A, work even until 6 ins. above cuff, decreasing 2 sts in last round; 40 sts.
Since you are working in one color this would be simplified to:
Dividing round: K 20 sts, leave on needles for back of hand; bind off next 22 sts in ribbing. Fasten off. (So you k20, and then bind off 22 in ribbing and keep the 20 that you didn't bind off on one of the dpns to wait till a bit later.) (Yes, finish off here after binding off the stitches. This is the top edge of where the mitten opens up on the palm.)
Underlap: Cast on 22 sts, k 1 row, p1 for 16 rows. Break off.
(I believe these 22 stitches are cast on to a separate needle and worked for the 16 rows. They are a completely separate piece until you join it to the other part in the next step. And I do think you need to cut the yarn there like it says because you start in a different place next.)
Joining round: K 20 sts of back of hand (these are the 20 stitches you left on a needle for the back of the hand on the dividing round.)
, join (this means you are starting to work in the round again)
and k 22 sts of underlap (that is the separate piece that you just knit a minute ago)
; 42 sts. (You will be joining the stitches from the back of the hand to the separate piece you made, after you get it all joined you will be working on 42 stitches just like the finger part of a regular mitten.)
Knit until 6 ins. above cuff, decreasing 2 sts in last round; 40 sts.
Then at the end the pattern says to finish do this:
FINISHING: Steam. Sew side edges of underlap to side edges of palm.
I don't picture this completely. I guess you stick that flap part down inside the palm of the mitten and then sew it just on the edge to the inside of the palm.
These are my thoughts. Maybe they will help you figure out what you have to do. I may not be right, but sometimes even a wrong answer helps you figure out the right answer. :-)