I figured since I get asked this question a lot, I should just put all the information in one place.
Wikipedia states: "Breast binding is the material used in, or the act of reducing visible breast size in both women and men through the use of constrictive materials."
In pre-operative FtM transsexuals, transgendered persons, genderqueer and crossdressers, this is done to minimize the breasts as much as possible, and to give a flatter, more masculine appearance, or the appearance of male pectoral muscles.
Depending on your breast size, this can be done a number of ways, some relatively safe - such as sports bras and binding vests - and some incredibly dangerous, like duct tape. My personal preference is for the binding vests from Underworks. I own the 997 model, and it does a fairly good job at compressing my 38DD chest. I'd like to get a second vest (possibly the 980) and layer them for additional compression. I'm worried at how hot these are going to be in the Florida summer *cringe*.
Binding takes time. It takes time not only to get into your binder, but to figure out exactly the best way to wear it for you, and to get comfortable with it. I'm not going to lie - binding can be incredibly uncomfortable at times. If it pushes on your stomach it can make eating a pain, and if you don't sit properly it can really cause an ache in your back. You need to keep at it, keep experimenting, and find out the most comfortable method for you.
Once I get moved, I'll post before and after pictures of my specific binding, and how effective it is. For now I'm going to post what resources I have collected below for people who are interested in learning more about different binding methods. As many will state, I really do recommend getting a binder, and not using tape or elastic bandages, which can be incredibly painful and hazardous to your health.
Hudson's Guide to FtM Binding
FtM at Underworks
Tip For Keeping Binders from Rolling Up
Breast Binding Photos before Testosterone
Hope this helps anyone who was interested. If I find any other links of interest I'll post them asap. Good luck!