I've never used razors to cut my wigs. I use scissors, a pair of the cheap ones intended for trimming hair. You can usually find them in the grocery store in the household aisle (near the thread and clothespins) or at your local dollar store. I think scissors would give you better control than a razor.
Other stuff you'll need: foam or plastic curlers, aquanet (the cheap hairspray, costs about two bucks; I've never use got2b, so I don't know how well it works), long straight pins (the kind with the colored knob on the end), a wide-tooth comb, a hair dryer with a low-temp setting. If you can get it, a foam wig head (check Display & Costume or someplace that carries wigs), or some sort of weighted item to keep your wig on while you're styling it.
First, to reduce the inward curl, you'll want to treat with hot water. Anything waterproof that can hold the wig up will work. Place the wig on its form in the bathtub. Dump hot water (not boiling) over the wig several times. Allow to sit with the fibers hanging free for a couple of hours. You can blow dry the rest of the way, just use the low-temp setting. Don't comb your wig until it's dry, or the fibers will really start to come out.
For the next step, it really does help to have a wig head to pin the wig to. First you want to make your bangs. Comb the amount of fiber you want to turn into bangs forward so it's hanging over where your eyes will be. Comb gently. Pick how long you want the bangs to be, then trim the fiber at least an inch and a half longer than you need. Try the wig on now and see what it looks like. Do the bangs need to be evened up? Do they not hang forward properly? If it's the second one, and the bangs are hanging off to the sides (it can happen when your wig has a part in the middle), spritz the roots of the bangs with a little hairspray, pull them forward, and then hit the roots with the hair dryer until the spray dries. You'll want to hold the dryer a little close to the fiber; it'll soften the hair slightly, essentially "melting" it in the direction you want. Keep working at the bangs until they look the way you want them too. Remember, it's better they be a little too long than too short. Longish bangs look cute. Short bangs on a wig make the wig look cheap.
To do the side pieces, spritz a little hairspray on your hand and run it down the piece a couple of times. Work especially on the ends. You might not be able to get the same sharpness, but it'll keep the piece pretty well together.
Now you want to do the flip. Work on one small section at a time and take your time. Spritz the ends of the hair with hairspray and wind a curler halfway up the length of the hair. Make sure you're winding it so the curl will point out, not in. Close the curler and if you're working on a wig head, pin it in place. Use the hair dryer to dry the spray. Then leave the curler in at least until the fiber has cooled completely. Work on the other sections of hair. Once they've all been done, walk away. Just leave it alone for a bit. Go watch an episode of your favorite series or work on the other parts of your costume. When you come back, take the curlers out. Make sure your hands are clean. Work your fingers through the ends, separating any major snarls (gently!). Then carefully comb through the ends. You can even brush it a little, just be gentle and work only on the ends. Continue to work until the curl has settled into a flip. Set the style with hairspray (focus on the ends). Let dry completely.
To keep the bulk of the hair tucked behind your ears while you're wearing it, you can use hairspray or some wax or pomade.
Make sure you wear a wig cap underneath. They sell them at Display & Costume, but you can also make one out of an old pair of nylons (so I've heard). Get a neutral-colored one. And to hold the wig in place, I'd suggest hair pins, the V-shaped ones (not bobby pins, which are flat).
To keep your wig nice, comb it gently after you've worn it and store it carefully (on a form or head if you can). A bottle of wig spray/conditioner is also a good investment, especially if you start to buy longer wigs.
