Hat and Scarf

Materials you will need:

Worsted weight yarn in the color(s) of your choice
Crochet hook appropriate for your yarn (check the yarn label for recommended hook size)
Scissors
Yarn needle for weaving in ends
Crochet Hat:

Start by making a slipknot and then chain 4. Join the last chain to the first one with a slip stitch to form a ring.
Chain 3 (counts as the first double crochet stitch), and then work 11 more double crochet stitches into the ring. You should have a total of 12 double crochet stitches.
Slip stitch to the top of the beginning chain 3 to join the round.
Chain 3, and then work 1 double crochet stitch into the same stitch as the chain 3. Work 2 double crochet stitches into each stitch around. Slip stitch to the top of the beginning chain 3 to join the round. You should have a total of 24 double crochet stitches.
Chain 3, work 1 double crochet stitch into the next stitch, then work 2 double crochet stitches into the following stitch Repeat from * to * around. Slip stitch to the top of the beginning chain 3 to join the round. You should have a total of 36 double crochet stitches.
Continue this pattern, increasing the number of double crochet stitches between increases, until the hat reaches your desired size. For example, in the next round, you would work 1 double crochet stitch into the next 2 stitches, then work 2 double crochet stitches into the following stitch Repeat from * to * around. Slip stitch to the top of the beginning chain 3 to join the round.
Once you’ve reached the desired size, you can work even rounds without increasing until the hat is tall enough. Continue working rounds of double crochet stitches until the hat is the desired length, usually around 6-7 inches.
To finish the hat, cut the yarn, leaving a long tail. Thread the tail through a yarn needle, then weave it through the stitches of the last round, cinching it closed. Fasten off and weave in any remaining ends.
Crochet Scarf:

Start by making a slipknot and then chain a multiple of stitches to achieve the desired width of your scarf. A common width is around 8-10 inches.
Chain 3 (counts as the first double crochet stitch), and then work 1 double crochet stitch into the 4th chain from the hook. This creates your first row of double crochet stitches.
Chain 3, turn your work, and work 1 double crochet stitch into the next stitch. Continue working double crochet stitches into each stitch across the row.
Repeat step 3 until your scarf reaches the desired length. You can make it as long as you like.
To finish the scarf, cut the yarn, leaving a long tail. Thread the tail through a yarn needle, then weave it through the stitches of the last row to secure it. Fasten off and weave in any remaining ends.