Please note: This method is for Sitting There lace, not Wearing Around lace, and the material is COTTON, not wool or silk. Try this with a Kid Silk Haze shawl, and you will have an unholy mess on your hands and probably wind up having to throw all your beautiful work away. So be advised. This method is for Damn Doilies in cotton, only!
The pattern shown is "Coronet" from "The First Book of Modern Lace Knitting" by Marianne Kinzel. Avaiable at Amazon. Her second book is also cool. They seem to be based on Elizabeth Zimmermann's "pi shawl" method of knitting a circle from the center out, and truly new in terms of doily knitting, but the history of doilies is an entry for another day (when I'm sure it won't put everyone to sleep).
So wash your doily and then put it into a bowl full of cool water and liquid laundry starch. You can follow the directions for use on the bottle of starch, or just dump some in. I use the just dump method, and probably use a half cup of starch for a half gallon of water (this is way more than the directions say). In the past I have used watered-down Elmers' Glue in a pinch, and that works, but it takes FOREVER to dry and is really stiff. (REALLY stiff. But you can't beat it for blocking things you want to stand up.) Traditionally sugar and/or flour were used to stiffen lace, but that draws bugs to nibble on your hard work. And if you want to turn your white lace to beige, dunk it in a bowl of iced tea between the wash/rinse and the starch. (This is a one-way process.)
While your lace is sitting in the starch, get out a kazillion straight pins (I suggest the ones with the colored balls on the heads, so you can hang on to them) and a blocking board. You can spring for a regular blocking board, or you can use a chunk of foam-backed 'core board' from the art store. I use core board but when this one dies (water from repeated blockings eventually does them in) I'm getting a real blocking board. The usual lace method of putting it on the bed and pinning doesn't work in this case: The piece has to be stretched a LOT.
Fish your lace out of the slime (excuse me - starch water) and roll it in a towel and press on it to get the worst of the water out, then plop it on the board and locate two points opposite each other. (NOTE: Patterns with odd numbers of points are a TOTAL BITCH to block because they aren't symmetrical in any way and NOTHING lines up. Keep it in mind when picking a project.) Pin the two opposite sides down. I'd done this pattern before and written down how big it should be, so I cheated and measured.
After that, you figure out how many other points you have, and pin them out in approximately the right places. (This one has six points, so you have to eyeball it. If it had, say, eight, you could do the points at right angles, and then make the others fit.) At this stage (at any stage, really) this is not exact, and the points will be jiggered around some, but try to get it right.
Don't only measure across the doily, but measure between each point, to make sure you've got it somewhere close to right. (These were off by maybe a half inch, depending, when I measured, and that was close enough.) You CAN get out a protractor and draw six-pointed stars and block the points properly, but I've done it and it's an awful lot of bother. (If you look closely, that bottom point is crooked. It gets fixed, later.)
Pin out the other points, working on opposite sides as you do it, and remembering the doily is supposed to be ROUND, not hexagonal. (The husbeast says, 'this is like torquing down a tire' for those of you who are mechanics.)
From here, you start pinning out the little crochet loops you made when binding off. Do one at each side of each point, first.
And then you pin down all the other little points. Remember, the doily should be stretched TIGHT, and it's okay to move things around a little bit to make them balanced.
And there you go. Leave it alone until it dries, pull out the pins, and you have a doily. This method can be tweaked a little bit, and you can take doilies you knit round and block them into ovals. If you're desperate for a thrill, it's kind of fun.
Go knit some lace, try this for yourself, and send me pictures!