A hat is one of the best second projects in knitting. It is small enough to finish fast, and it teaches you shaping. Every pattern below is free on its designer’s own site and written with beginners in mind.
The first two are knit flat on straight needles and sewn up the back, so you can skip circular needles for now. The next three are knit in the round. Chunky yarn makes the first few very quick, while the worsted options take a bit longer and come in more sizes. Seven DROPS hats close the list, mostly simple rib or stockinette with a fold-up brim, in sizes for most adult heads.
Free beginner knit hat patterns
1. Easy Bobble Hat
Designer Helen Stewart at Curious Handmade. With a gauge of just 8 stitches to 4 inches, this hat grows fast. Helen uses one ball of Rowan Big Wool or two skeins of Blue Sky Alpaca Bulky on 10 mm (US 15) straight needles. You knit it flat, shape the top with k2tog decreases, then seam the back with mattress stitch and add a pompom. Sizes run from baby (14 inches) to man (22 inches) head circumference. Helen asks only that you already know the knit and purl stitches, and explains how to measure a head for the right size.

2. How to Knit a Hat with Straight Needles
Designer Louise Bollanos at Handy Little Me. Not ready for circular needles? This ribbed hat is knit back and forth on 6 mm (US 10) straight needles, then joined with a mattress-stitch seam. Louise uses a bulky wool and lists a gauge of 16 stitches and 20 rows to 4 inches in the rib. Seven sizes cover baby (0 to 3 months) up to adult large. The stitches are knit, purl, k2tog and p2tog. There is a step-by-step photo tutorial plus a video, and the full pattern is on the page. A printable PDF is sold separately.

3. Easy Beanie Knitting Pattern
Designer Jennifer at Brome Fields. This one is a gentle first step into knitting in the round. It needs only 45 to 55 yards of super bulky yarn, such as Cascade Magnum. Jennifer uses 10 mm (US 15) and 12 mm (US 17) circular needles, with double-pointed needles or a longer cable for the crown. The gauge is 7.5 stitches and 11.5 rounds to 4 inches, and it comes in one size for a 20 to 22 inch head. Only knit, purl and decreases are involved. The designer rates it beginner, and an ad-free PDF is optional.

4. Quick and Easy Knit Hat
Designer Tanya Eberhardt at Little Things Blogged. Six sizes, from newborn (13 inches) to adult man (22 inches), make this a handy pattern for knitting gifts for the whole family. You start at the brim with k1, p1 rib, then knit plain rounds and close the top by threading the yarn through the last stitches. Tanya uses a worsted yarn on 7 mm circular needles with a 16-inch cord, at 14 stitches and 22 rows to 4 inches. One honest note from Tanya: the hat tends to stretch, so the designer suggests going down a size for a snug fit.

5. Easy Knit Beanie Hat Pattern for Circular Needles
Designer Janine at Craft Fix. This worsted beanie comes in eight sizes, from newborn baby to XL adult, so you can knit it for anyone. It has a k1, p1 ribbed brim, a stockinette body and k2tog decreases at the crown. Janine works it on a 5 mm (US 8) 16-inch circular needle, at 18 stitches and 24 rounds to 4 inches. The designer calls it a good first circular-needle project. A free printable PDF is linked. The pattern is for personal use only, and finished hats may not be sold without permission.

6. Washed Tide Hat (DROPS 270-20)
Designer DROPS Design, free on the DROPS website. A hipster-style hat with a double fold, knit in the round in DROPS Air on 3.5 mm (US 4) needles, or with the Magic Loop method. It fits heads of 56 to 60 cm (22 to 24 in) and needs 100 g (3½ oz). The North Sea blue sample is a calm everyday color.

7. Polar Fold Hat (DROPS 270-15)
Designer DROPS Design, free on the DROPS website. A ribbed hat with a deep 10 cm (4 in) fold-up, worked with DROPS Alpaca and DROPS Kid-Silk held together, or DROPS Nord with Kid-Silk. Rib is only knits and purls, so this is a friendly first hat in the round. It fits heads of 54 to 58 cm (21 to 23 in).

8. Winter Smiles Hat (DROPS 214-67)
Designer DROPS Design, free on the DROPS website. A ribbed beanie with a 10 cm (4 in) fold-up, knit in DROPS Air. One 100 g (3½ oz) batch is enough for sizes S/M and L/XL, which fit heads of 54 to 58 cm (21 to 23 in). The pattern suggests brown, beige, moss green or sage green.

9. Fawn Frill Hat (DROPS 270-17)
Designer DROPS Design, free on the DROPS website. A stockinette hat with a double fold, worked in DROPS Melody, a soft, fluffy yarn, on 5.5 mm (US 9) needles. It fits heads of 54 to 58 cm (21 to 23 in) and uses only 50 to 100 g (2 to 3½ oz), so it knits up quickly.

10. Fall Air Hat (DROPS 270-10)
Designer DROPS Design, free on the DROPS website. A plain stockinette hat with a fold-up brim, knit bottom up in DROPS Lima or DROPS Karisma on 3.5 mm (US 4) needles. It fits heads of 56 to 60 cm (22 to 24 in) and takes 100 g (3½ oz). The wheat-colored sample goes with any coat.

11. Isle Waters (DROPS 234-9)
Designer DROPS Design, free on the DROPS website. A top-down beanie in stockinette with a folded brim, knit in DROPS Air on 4 mm (US 6) and 3.5 mm (US 4) circular needles. It comes in three sizes for heads of 54 to 60 cm (21 to 24 in), and one 100 g (3½ oz) batch covers every size.

12. Frosted Rose Hat (DROPS 270-9)
Designer DROPS Design, free on the DROPS website. A soft hipster hat worked with DROPS Alpaca and DROPS Kid-Silk held together, or DROPS Nord with Kid-Silk. The pattern shows it in ice blue, dusty pink and wheat. It fits heads of 56 to 60 cm (22 to 24 in).

Not sure what k2tog or mattress stitch means? My Knitting Stitches Guide explains the stitches and abbreviations these hats use.