This is my experience in learning how to cut bangs into a wig. This isn't in a 'step by step' photographed format because I was just learning and this took me several hours of trial-and-error.
The first cut...
I took an Enchantment wig and parted out the part that I wanted to cut. I parted it about one inch back from the front hairline and combed that forward in front/center and took a little bit from the sides of the front with them. So, it's a straight line that curves somewhat parallel to the hairline. Look at photos of people with bangs to get the bang length that you'd like. If you don't go back enough, you'll have only very wispy bangs. That wasn't what I was going for though. =)
Heat it and push it
I made an initial cut - much longer than I wanted the bangs to be. I then pulled all the rest of the hair back. It's much easier when they're out of the way!
Then I took my handy blow dryer and, while pressing the bangs straight toward the front blow dried them on low heat. Use your own best judgment, you don't want to melt the hair, you just want to heat it. After you're done, walk away and let it cool completely down.
Curl it under (or up)
I used clippers, but you want to cut the remaining hair in a straight line. I recommend separating the hair into a top and bottom layer, and cutting the bottom a bit shorter than the top layer if you want the bangs to curl underneath. I kept working at this until they were a little longer than I wanted, since when they're curled under slightly, they'll be a little bit shorter.
Set it and smile!
I did two steps to get the bangs to curl under slightly. I hairsprayed the bangs slightly, then put an end paper (like you use for perms) on them and rolled them under. I put a small curler in them and T-Pinned them to the wig head to keep them steady. Then, just like in the essay on how to curl hair, I put a blowdryer on them, heated them up while on the roller and let them get cool before I pulled them out (that helps set the curl).
I removed the rollers and brushed the curls out a little bit.
I then used an adjustable temperature curling iron, set it on 3 and curled the hair. It's very important that you not use a full temperature curling iron on your hair. The best setting should be warm to the touch
Then, curl under just the ends. Keep working at them, never leaving the iron too long in the same spot, or else the tension of the iron can cause horizontal lines in the wig hair. Think of this as the equivalent of blowdrying natural hair and curling it under with a round brush (you can do this too with your wig, but I found it slower)
I hairsprayed the bangs into place. Then I made sure I wasn't going to move them, and then I did a final trim of 'scraggly' ends.
This is just a log of my experiences - your own experience may vary. I always assume that you are very experienced and I'm a n00b, but I write as if I'm confidently talking to you. It doesn't mean that I know everything. =) Be gentle with your wig and always have fun! =)