ETA: I did NOT knit any of the doilies used as examples in this info. I HAVE knit the banded doily pattern, but the one in the photo is not the one I knit. All were skimmed off Ravelry. A search of 'doily' in 'patterns' will turn them up.
That's the usual technical term used for, among other things, doilies. Anything that is started with a few stitches and knitted outward in all directions, and winds up flat at the finish, is a medallion. Pi blankies, coasters, nearly all round and quite a few square shawls, you name it, they're medallions. Doilies and some shawls are more properly known as lace medallions. You get the idea.
So here's what I know about knitting lace medallions. Quick history, then a section on 'what makes it hard/too much bother'.
According to the history books I've read, the oldest known doilies were knit flat, on two needles (and therefore technically not medallions, but work with me here). They looked something like this:
You'd cast on stitches for the radius (center to the edge) and then knit each wedge in short rows - that's right, lace short rows - and when you got back 'round to where you started, you grafted them together - that's right, grafting in lace. I keep meaning to knit one of these to say I did it, but then I think 'lace short rows' and go cast on something more rational. Like a Dale of Norway cardigan.
The above short-row pattern dates to a 1917 knitting pattern put out by a thread company, and patterns like this are said to date back to the Victorian era. The common thinking is, the Victorian ladies didn't have thin enough double point needles to knit true, center-out lace medallions and so used single-points and short rows instead. To me this theory is SERIOUSLY flawed, what with all those twenty-stitches-per-inch circularly knit stockings dating back to the 1500s. Obviously SOMEONE had the needles to knit regular doilies. Personally, I think the short-row doily was nothing but a fad. Thrill knitting, as it were.
So. 'Real' doilies. Cast on a few (four to twelve, in my experience) stitches and start knitting outward in all directions. Usually round, but not always. Usually the bind-off is done with crochet slip-stitch (the only crochet I am remotely proficient at), but occasionally someone goes crazy and knits on a sideways edge.
These have never been reliably dated, that I could find, but they certainly go back to Victorian times, and I suspect are an offshoot of lace caps. (You know, those mushroom-like 'mobcaps' that women wore on their heads all the time.) Those were pretty much doilies with a draw string. Not much of a leap to a decorative mat. Just some starch. Jane Sowerby (Victorian Lace Today) puts the date of her earliest medallion shawl at 1840, which sounds about right from all I've been able to dig up over the years. I'm betting they go back to the late 1700s, at least, but so far I haven't been able to find any refrences, that's just my own sneaking suspicion. (The suspicion is based on what I know of lace and fashion of the day.)
The third and most recent type of doily has appeared since the 1950s, and I am POSITIVE are based on Elizabeth Zimmermann's Pi shawls. For those who haven't seen or knit one, a pi shawl is a round medallion knit on the basis of pi for the increasing; every doubled number of rows, double the number of stitches. In other words, cast on, say, six stitches. Knit a round. Increase to twelve stitches. Knit two rounds. Increase to twenty four stitches. And on and on, until you've knit the Hindenburg. Fill with hydrogen and look out for American saboteurs.
What you wind up with is a circle knit in bands, and it doesn't take much to go from there to lace patterns and you get something like this.
You see a significant bulls-eye effect happening. There's no lateral motif that stretches from the center to the edge, as is normal in older medallions. This is based entirely on the pi system, and I have seen pattern books that switch out bands and are modular; pick the bits you like and knit in order.
As for difficulty. Charted patterns are the way to go. With the way these SPECIFIC patterns are normally charted, some of them can be read left to right and knit successfully, if that's what your big hangup is with knitting charts.
There are many, varied and complicated fiddly little cast-ons for medallion knitting. I've tried them all. These days I use a provisional cast-on (the usual long-tail method with contrasting yarn). After I'm done knitting and am darning in ends, I pick out the provisional cast-on and thread the tail of yarn through the stitches. Pull tight. Finish off. Like the top of a stocking cap. Easy as heck, looks all impressive like you are a cast-on goddess.
For sitting-around lace (table cloths, decorating whatever) I suggest using something strong, like cotton or linen. They take a beating and a washing and re-starching without a problem. For wearing-around lace, heck, use whatever you want. I like alpaca and silk for shawls, they drape very nicely. Mohair drapes well too, if you can stand it. All three are very warm.
Needle size is up to you, particularly on doilies, but size twos are a good place to start. Small enough that it looks like lace, but big enough you can see what you're doing.
Choosing a pattern is really the tricky part. Banded doilies, like the one I discussed last, above, are not only easy, but easy to fix, if you screw them up. Off by a stitch or three? Just increase at the next band/pattern shift. Looks fine. A word of warning, though. DO NOT KNIT ONE OF THESE IF THERE IS AN UNEVEN NUMBER OF SCALLOPS ON THE EDGING. I once nearly lost my mind trying to block a thirteen-point round doily. Nothing was symmetrical. Avoid this. Not worth it. Never worth it.
Traditional doilies are more impressive (if you ask me) and great fun to knit. If you're a little careful about picking your pattern, you're golden. As you know, these types are knit in repetitive pizza-slice shaped bits, repeated around the circle:
You get a chart for one slice, and repeat it as many times as the pattern tells you to. Obvious. Easy. This is how I'm knitting patterns written in German; count pattern repeats around, get the chart, let it rip.
Here's the secret. The more slices of circle, the smaller the slice is, and THE EASIER IT IS TO REMEMBER. Which means you won't be staring at the chart constantly, which means you will knit faster. The one I'm doing now? Aster?
Sixteen repeats. By the third or fourth go, I remember it and knit like the wind.
Something like this?
Four repeats. You will sleep with this chart and still not remember from one repeat to the next.
Occasionally you can cheat. Lyra, the doily I want to knit for my mother-in-law? It's sneaky. It's really an octagon. There are little bits knit on in the corners (outlined in blue) to make it a square. So it's easier than a true four-repeat square.
There you are. Doily knitting. Now all of you know my secrets and will never be impressed again.
Gotta go knit. I'm gonna do beads soon.