I recently helped one of my friends attach the sleeves to her Bellyphant baby sweater, and I admit, it is a little hard to wrap your brain around what you're doing the first time you do this. What you have when you join the sleeves to the sweater body is two small tubes and one large "tube" that is not a tube because it is a cardigan. The difficult thing to imagine beforehand, but what becomes really obvious once you've done it, is that when you're holding a sleeve tube up next to the sweater to attach it, the back side of the sleeve (closest to the armpit) is held with right side facing the right side of body, and the outside of the sleeve is held with right side facing out. So the stitches you are binding off at the armpit are bound off with right sides facing -- using the tail end of the yarn you used to knit the sleeves -- and then you use the working yarn from the body section to knit around the outside of the sleeve all the way to the other side, and then continue working the back of the sweater.
The diagrams in this Vogue Knitting article by Jared Flood help to clarify this all. Jared has you put the armpit sleeves on holders rather than binding them off. If that is easier for you, by all means, do it his way. For me, I like as little finishing as possible, so I like the three-needle bindoff.
So here's the process as I am working that row where the arm stitches are joined:
First I knit the right number of stitches of the body section for the cardigan front. Then I hold my sleeve up to the body section. (I've been working the sleeves magic-loop, so half the sleeve stitches are on one side of the circular needle and half are on the other, and the two needles are both facing with the points to the right.) I use the length of yarn that's hanging off the sleeve stitches to bind off the right number of stitches of the body and the sleeve together with three-needle-bindoff. The sleeve needle that I am binding stitches off of is the back needle of the sleeve (the one that has purl stitches facing me as I am looking at the sleeve tube). After I've finished binding off these stitches, I knot that yarn from the sleeve and drop it. Then I pick up the working yarn from the body section and continue knitting across the sleeve -- but this time I knit across the top needle of the sleeve (the one that has the knit stitches facing me). When I have knit all the sleeve stitches, I go on across the back of the body section until I get to the next sleeve and repeat the process.
Does that help at all? It sounds really hard until you do it. It's hard to visualize ahead of time and to describe in words, but it's very intuitive when you are actually knitting.
Side note: some knitters on Ravelry have wondered why I designed this one bottom-up instead of top-down like the other raglan sweater patterns I've done. The answer is that there's a little bit of variability in people's row gauge, and if you are knitting the sweater top-down, it's hard to be precise about placing the elephants at the bottom and making sure that the sweater is the right length. If you start with the elephants, you can knit the striped part of the body as long as you need it to be before adding the sleeves -- the stripe is only a 4-row repeat but the elephants are something like 18 rows tall.