How do I knit a circle?

So I knitted my Grandpa a mug cozy, and as I was fitting it on the mug, I had a brilliant idea. What if I could knit a circle to work as a coaster, and seam it onto the bottom of the cozy? But Im not entirely sure how to knit a flat circle and my google searches came up blank. Would I need circular needles for it? Or could I knit it on straight needles? Is it even possible?

Take a look at this page:

Kitty pi bed

you could:

1- knit a parallelagram…
(cast on X, with a strechy cast on. knit flat (in any stitch),
increase every 4 row both ends.

when knitting is about 3 inches long, bind off.

sew sides seams, at top (cast off edge) and at bottom(cast on edge) leaving seam open at side. (for finger loop of mug)

2–or you could cast on, join into round work some rounds, (increase 2 times in every 4th round) for about 1 inch
then work straight, (not rounds) for 1 inch,
then go back to working in rounds for 1 inch and bind off

3–or you could cast on 8, join into round, work in rounds, increasing 8 stitches, evenly, every other round, till the flat is about equal to diameter desired. then work in rounds, for 2 or more inches, (increasing 2 stitches every 4th round,

if you want a tall cosy (for a mug) work an inch flat (turning work) to created vertical hole for finger loop, end by working in round again.

Another pattern for a circle. Its a felted coaster, you could leave them not felted if necessary.

Thanks for your help, guys. But I decided that since I finally finished the mug cozy, I just wanted to move on to other projects. In the time it would have taken me to just cast on the coaster and knit a few rows, I knitted a whole bookmark in stockinette for my best guy friend. Its currently sitting under a big pile of books and a dumbell weight in order to block it, lol. Thanks anyway, guys. I may use that coaster pattern for a birthday present for my dads best friend though.