- at the crown, with a few stitches which you increase, or
- at the brim, gradually decreasing the stitches.
You may also knit the hat as a flat rectangle, sewing the sides together and sewing across the top edge. This produces a square-edged hat, which may be worn in either orientation:
It is also possible to work a hat from one side, using short-rows with increases and decreases to the other side: designer Woolly Wormhead has explored this construction, and almost every other possible construction too.
Another possibility is to knit a hat in segments. The best example of this is the Fool’s Gold jester cap, which is the basis for my Borg Queen, or I Are A Pwincess Now:
There are other, more complex constructions (grins evilly) too.
BUT EVERY SINGLE ONE CAN BE KNIT ON CIRCULAR NEEDLES.
I use circs almost exclusively in preference to straights (‘normal’ single-pointed needles). This is because I have relatively short forearms and large biceps, and most straights are too long and either get stuck against my upper arms or whack them with every stitch. I’m in knitting for the pleasure, not the pain.
Circs can be used for small tubular projects like hats or socks by
- selecting a short cable
- using two circs:
- using a technique such as Magic Loop:
The latter two techniques can be used to work a hat from the crown down, starting with a few stitches, or when reducing the number of stitches for a brim-up hat.
For other constructions, a circ can be used just the same way that a pair of straights are used. Just knit a row, then swap the left and right needle-tips to the right and left hand respectively, and repeat.
PS: the foregoing works for socks, gloves, mitts, mittens, sweaters, scarves, trousers, toys, cushions, blankets, and everything that you can possibly imagine knitting.