Sometimes I like to use this pattern for a beanie ~ Head Hugger ~ though I do make a few little changes to it.
Like Jewel, I love to search Ravelry for free patterns

I'll try and write my most-used pattern here, it fits my 17 month old DS
(I've never written a pattern before, let me know if it doesn't make sense! Also, I think I use american style stitches?)


Chain 5, join with slip stitch to form a ring.
R1: Chain 3, 9 double crochet in the ring (CH3 = 1st DC, so 10DC total) Join with slip stitch to first chain 3
R2: Chain 3, double crochet in same stitch. 2 double crochet in each stitch around (20DC total) Join.
R2: Chain 3, double crochet in same stitch. *1 double crochet in next stitch, then 2 double crochet in next stitch. Repeat from * around so you have 30 double crochet total. Join.
R4: Chain 3, double crochet in same stitch. *1 double crochet in next two stitches, then 2 double crochet in next stitch. Repeat from * around so you have 40 double crochet total. Join.
R5: Chain 3, double crochet in same stitch. *1 double crochet in next three stitches, then 2 double crochet in next stitch. Repeat from * around so you have 50 double crochet total. Join.

Now I have finished increasing stitches, I just double crochet in each stitch around - joining at the end of each round - until I have the desired length.
Or I might stop just short of the length I want, and finish the beanie off with 2 or 3 rows of single crochet instead.

HTH!