These are most commonly done as "sandwich board" costumes, using sheet foam. I've done similar things many times, and they don't involve sewing. A hot glue gun comes in very handy, however. With this type of costume the child's head is essentially just ignored when it is sticking out of the costume; it is not expected that his head will be the creature's head.
For Sebastian you need a red turtleneck or long-sleeve T, for Flounder, you need yellow. Pants are not an issue if you make the costume large, which works best anyway. You can buy 1/3" thick sheet foam at most fabric stores.
What you do is to make a poster-board cutout template of the creature's 2-D shape, then cut two foam pieces with it. Cut any surface color changes out of the paper template, then use it with spray-paint to color the foam (like Flounder's blue stripes); or you can hand-paint them, if you prefer, using acrylic paints.
Then hot-glue the two pieces together at the sides, leaving the top and bottom open. Also glue on some ribbon "shoulder straps" that will allow the costume to stay up on the child's shoulders. (Note that with Sebastian, the front claws are your child's arms; you only need to cut the other prs. out on the foam. For Flounder, the arms get ignored just like the head, unless you want to cut holes in the sides and let him chicken-flap for "fins".)
