To knit a slouchy hat on regular (straight) needles, you will need to knit a flat piece, then sew one seam. Your cast-on edge will be the ribbing on the brim, and you will end at the middle of the crown.
Make a swatch to determine your gauge. Cast on 20 stitches and work in stockinet stitch (knit one row, purl one row) for 20 rows. Remove this swatch from the needles, pick a spot near the middle of your work and carefully count the number of stitches in 2.5 cm (1 inch) using a metal ruler. Alternatively, measure the entire width of your swatch, and divide the total number of stitches (20) by the total width of your swatch -- for example, 12.5 cm ( 5 inches). In this case, you have four stitches in 2.5 cm (1 inch).
Adjust needle size to achieve gauge. If your gauge was not four stitches in 2.5 cm (1 inch), change needles and continue swatching until you obtain the correct gauge. If you had more than four stitches in 2.5 cm (1 inch), you will need larger needles. If you had fewer than four stitches in 2.5 cm (1 inch), you will need smaller needles.
Cast on 80 stitches. Work in K (knit) 2, P (purl) 2 rib for 1 inch. Switch to stockinet stitch, and begin working increases, starting with a right side (knit) row. Increase row one: K10, make 1 (pick up the strand in between your two needles, place it on the left needle, and knit into this as if it were a stitch), repeat from * to end of row. Work three rows even. Increase row two: K11, make 1, repeat from * to end of row. Work three rows even. Increase row three: *K12, make 1, repeat from * to end of row. Continue working increases in this manner until hat reaches desired width.
Begin decreases. Decrease row one: K10, K2tog (knit two stitches together), repeat from * to end of row. Purl 1 row. Decrease row two: K9, K2tog, repeat from * to end of row. Purl 1 row. Decrease row three: *K8, K2 tog, repeat from * to end of row. Purl 1 row. Continue decreasing in this manner until 8 to 12 stitches remain. Cut yarn, leaving a 30 cm (12 inch) tail, and thread yarn onto a tapestry needle. Draw the tapestry needle through remaining stitches and pull tight. Sew back seam using a mattress stitch.