The first step in sewing your renfaire costume is to pick out a pattern. You will probably want something that has a bodice, skirt, and underdress (see below), and hopefully also some accessories like a hat, apron, or purse. The big three pattern makers—Simplicity, Butterick, and McCall's—all have extensive collections of historical costumes. Butterick #6196 is one good choice.
A word about pattern prices: the label on the pattern will have some ridiculous number on it, perhaps $14. Nobody in their right mind pays $14 for a pattern. Any half-decent fabric store will have a perpetual sale in which all patterns are 50% off, and if you wait for the right weekend, you should be able to get patterns for $1.99 or less. Usually only one brand will be on sale at a time, so plan ahead.
In a similar vein, there is no reason to pay a lot for fabric. Authentic-looking fabrics are all solid colors of very plain cloth. If we were being super-accurate, we would use wool or linen, but we aren't being super-accurate. We are being practical. Wool is heavy and expensive; linen is lightweight and also expensive. The fabric you want will be made of cotton or something similar; broadcloth and muslin are good choices. Quilter's fabric is especially good, because it comes in a huge spectrum of colors and is often on sale. Remember that the best stuff comes from the clearance tables. I made a complete renfaire outfit this weekend from about $10 worth of fabric. You can too!
You will want a sewing machine, because you do not have the time, much less the patience, to do all the sewing by hand. If you don't have a sewing machine, ask around. You are virtually guaranteed to have at least one older female relative (mother, grandmother, aunt,...) who (a) has a sewing machine, (b) is willing to lend it to you, and (c) is also willing to teach you how to use it. If you are totally bereft of older female relatives, and think you may sew again in the future, consider purchasing a machine. You can get a cheap one for $99.
You will also want to make sure you have a lot of time before the renfaire. I have made entire renfaire outfits in weekend-long marathon sewing sessions, but I do not recommend this, especially if it's your first time.
So, is this going to be easy?
Not really. You see, there are three main parts to the typical female renfaire outfit:
The underdress is usually white, usually with a ruffled plunging neckline and poofy sleeves. It should be floor-length if you are concerned about historical accuracy; the skirt is worn over this, so that you have two layers. But since most renfaires are held in the hot hot summer, and since nobody will see the lower half of the underdress anyway, many women opt for a cutoff version that is only as long as a shirt. Either way, this is easy to sew. Typically you will sew together a front, a back, and two sleeves. The ruffles at the neck and wrists come from elastic or drawstring that is inserted in a casing made from bias tape. The sewing is easy, and the ruffles cover mistakes well. (Of course, there are also patterns that don't make use of ruffles at all, and these are constructed a bit differently.)
The skirt is just what it sounds like, an ankle-length skirt that goes over the underdress. In the winter, you could pile several skirts on top of each other. Also, you may see some peasant women wearing the skirt tucked up on one side—this is to keep it from dragging in the mud. To effect this look, simply tuck your skirt into your waistband so that it no longer drags in the mud. Fancy contraptions involving elastic are not necessary.
A skirt can be anywhere from "medium-easy" to "accomplishable by a chimpanzee". For medium-easy, follow the directions in the pattern you buy. You will probably be cutting out trapezoidal pieces, gathering them into a waistband, and sewing a zipper in the back. Fine, if you're into that sort of thing. But I prefer the quick-n-dirty drawstring skirt, which you can bang out in less than half an hour. Listen up:
You want to buy around 3 yards of fabric. Less for a slimmer skirt, more for a really poofy one. Lay your fabric out. It will be 3 yards (or whatever) long, and probably 60 inches or 45 inches tall. Figure out how long you want your skirt to be, and add two or three inches for good measure. Cut the fabric so that it is now 3 yards long by $skirt_height high. Now all you have to do is sew the short ends together to make a cylinder, then fold (and sew) one long side—the one you just cut—so that it makes a casing you can put the drawstring through. You'll notice that the other long side of the fabric, now forming the bottom of the skirt, doesn't need to be hemmed - it is a selvedge, which naturally doesn't unravel.
The bodice is the most difficult part of the ensemble, and is actually one of the most difficult garments to make, period. It's pieced together from eight pieces of fabric, and lined with an identical version of itself. There are usually also layers of fabric or interfacing sandwiched inside, for stiffness. Oh, and many include boning. Boning (named after whalebone, which it is no longer made out of) looks like strips of plastic, sometimes encased in fabric sleeves. It's used to stiffen the bodice even more. A proper bodice is very supportive (no need for a bra) and very stiff; but if you prefer, you can easily make a softer, more comfortable bodice by leaving out the boning and not using too many layers.
A bodice starts out as a big pile of tiny bits of fabric. Some are for the outside, some are for the lining. Some are left, some are right. Some are back, some are front. You WILL get them mixed up. Many times. You will be almost finished with the front left part of the bodice when you notice you sewed something in upside down. You will be ready to unite the right and left halves of the back when you notice that you actually sewed two left halves. You will also wonder how in hell you are supposed to sew a concave edge to a convex edge. Use a ton of pins, match up every last notch and dot, triple-check every seam before you sew it, and you'll come out OK.
Don't forget to accessorize. Back in the day, it was embarrassing to go outdoors without a hat - so make yourself a cap out of whatever scraps you have left (you can find simple renfaire hat patterns on the 'net), and make a pouch to keep your money in.