Before I knew how to properly cut a bell pepper, the tiny white circular seeds would explode everywhere but where I wanted them: in the trash. I don't remember where exactly I learned to chop bell peppers, but this method will save you from a mess of seeds, as well as preserve the most amount of tasty bell pepper for your dish (or for snacking).
Step One: remove the top
Cut usable pieces from the top. This limits waste and gives you more to work with (or snack on). Win-win. My bell pepper's stem fell off as I cut the top off, but if that doesn't happen, cut pieces of pepper away from the stem.
Step Two: cut each section away from the ribs
Place the pepper cut-side down. You should be able to see the natural sections of the pepper. Usually there are 3-4 sections. Place your knife close to the center, and cut downward, following the section down to your cutting board. You can see that this method avoids all ribs (white membrane) and seeds.
Once you've cut all the larger pieces away, you can discard the middle. Look at how much bell pepper you have to work with! Any rogue ribs can be torn or sliced off.
Now you are ready to chop, mince, or julienne without worry.