Often new knitters shy away from knitting anything but simple scarves when choosing projects. However, just like scarves, beanies are easy to knit. All you need to know are the two basic stitches of knit and purl. Although beanies are commonly knitted on circular needles, they can also be knitted on straight ones. Often knitting with straight needles is simpler than knitting on circular needles as it's easier to correct a mistake such as dropped stitch.
Determine how many stitches are needed to cast on for the beanie's circumference. To do this, check the information regarding the gauge, found on your yarn label. For example, when using size 8 needles on 4-ply (medium-weight) yarn, you get 17 stitches for a swatch that is 4 by 4 inches. The average circumference for a 3-year-old toddler is 20 inches; therefore, it will take five 4-by-4 inch swatches for the circumference, for a total of 85 stitches.
Cast on 85 stitches. As for a design, you have several choices. You can use a stockinet stitch with alternating knit and purl rows, a garter stitch where you knit every row or a ribbed stitch of alternating knits and purls within rows. For simplicity, use the garter stitch, knitting every row.
Continue knitting rows until your beanie measures about ¾ of the size of the total hat. A beanie for a 3-year-old is about 8 inches tall, so shaping would begin when the piece is about 6 inches long.
Start shaping the beanie by gradually decreasing the stitches in each row. Decrease rows symmetrically, decreasing the same amount of stitches at the beginning and end of a row, such as one to two stitches.
Bind off at the point where you have only a few stitches left on the needle (about 4 to 6).
Sew the seam, with right sides together. Turn the beanie to its right side and give it to that special grandchild or other toddler in your life.
If you don't want to decrease stitches at the beanie's crown for shaping, you could continue knitting the same amount of stitches. After sewing up the seams, take yarn and weave (about 2 inches from the top) to gather stitches, decreasing the width. Pull yarn tightly to form the crown of the bean. Change yarn colours, alternating rows, for more contrast.
Watch for dropped stitches and if you find one, use a crochet hook to pick it up (see Resources).