What type of equipment will I need to start fly fishing?

Never fly fished before in my life. I have a Rod/Reel combo with line and a leader. And I know I will need waders, a vest, and a net. After that, I'm lost. What other essentials should I have to start out?

I am big on starting simple especially with fly fishing but I listed some must-haves and some optional items below. My additions to GMB's list are as follows:

- You are going to need a flybox
- You will also need a hemostat or pliers to get the hooks out
- You may want to have some dry fly dressing if you are going to be using flies on the surface
- You could bring split shot for getting flies down deep
- Polarized sunglasses will help you to see fish

*Optional items would be strike indicators for nymphing, sinktips for streamers and other subsurface flies but really you wont need these right at the start unless you are doing something specific ie fishing wet flies for steelhead / salmon.