The Sponge Bob hat used a combo of a crocheted nose, felt eyes and mouth that were hand-sewn onto the hat using bonbon yarn and various types of stitches.
I used my sons stuffed Sponge Bob toy as the example to follow the details. Please use an example of the Sponge Bob to help you with the details when performing the embroidery. I had the stuffed toy with me at all times to refer to while working on the hat.
For any help with embroidery details, check out this Instructable: Embroidery 101.
Note that in several of the photos, I show the INSIDE of the hat.
Crochet Nose Pattern
Use smaller hook size from gauge (in my case it was a G.)
Rnd 1: 6 hdc in 2nd ch from hook, sl st in top of first hdc.
Rnd 2: Ch 1, hdc in each st across (6 hdc sts)
Rnds 3 - 4: Repeat rnd 2.
Finish off, leaving a long end for sewing.
Note that the nose gets sewn on LAST.
Cut Felt Pieces
In all cases, I tried to trace any pieces on the backside of the felt (I looked for the sticker.)
The eyes use white, black and blue felt. Make two.
I used the end of a baby food jar to trace the white part of the eyes, a chapstick end for the black part (pupil) of the eyes, and used a circle template to trace the blue part (iris) of the eyes.
For mouth, tongue & teeth, it uses red, pink and white felt.
I used the now-cut eyes as a basis to determine how wide to make the mouth. I hand drew the mouth based off of the look on the Sponge Bob stuffed toy we had. I folded the red felt in half and cut the mouth around the half to make both sides look even.
I hand-drew the tongue on the pink felt, using the bottom of the mouth as a guide for the bottom of the tongue.
I also hand-drew the teeth on the white felt, trying to cut them as equal as possible.
Embroider the Eyes and Mouth
I used the black embroidery thread to sew all the eye pieces and mouth pieces together.
I used a back and forth stitch, similar to a back stitch to sew the black pupil to the blue iris.
I then sewed the blue iris to the white part of the eye.
The hard part was making both eyes and all the pieces as even or equal-looking as possible. (I came pretty close!)
I started with the teeth on the mouth and continued to use the black embroidery thread to sew the teeth to the mouth.
Next I sewed the tongue onto the mouth, and I skipped the bottom of the tongue because I knew I was going to sew it to the hat.
Sew the Eyes & Mouth to the Hat
I pinned the eyes to the hat prior to sewing to keep them in place.
I used the black thread and a blanket stitch to sew the eyes to the hat.
After sewing both the eyes down, I pinned the mouth to the hat and sewed that down using a blanket stitch.
Tie all loose ends on the inside of the hat and weave under the felt.
Embroider the Eye Lashes
I started from the center of the top of the eye and with the black thread, I sewed a satin stitch over about two rows. They are just about 1-inch long.
I made three passes to create the one eyelash and moved about one-quarter of an inch (1/4-inch) to make the other two eyelashes on either side of the center.
Embroider the Cheeks
Using the red thread (came from the Lion Brand Bonbons pack) the idea was to make a half-circle, similar to the stuffed SpongeBob, near the base of the eyes.
I began in the row below the eye I was working with, and made seven (7) about 1/4-inch long stitches to create the half-circle. When I did the first pass and was satisfied with the result, I went back over each stitch using a back stitch the entire time.
The little dots inside the cheek were done with french knots.
Sew on the Crocheted Nose
The very last step so it's not in the way while doing the embroidery details, take the long end of the crocheted nose and center it between the eyes, beginning about the same row as the lowest point of the eyes.
When sewing, try working into the nose area rather than stitching outside of the nose, so that the yarn-stitches are not visible if the nose gets pulled in any one direction.