I usually use a chef knife or a santoku knife depending on my mood or what else I'm cutting. It doesn't really matter. :)
Using the tip of the knife, slice around the stem, and carefully slice each side of the pepper so it will split in half.
After splitting it, remove the "core" with your hands. Shake the halves over the trash and/or rinse them under cold water to remove the remaining seeds.
After removing the seeds, you're ready to cut!
I usually slice lengthwise, and often then cut the slices in half (as pictured) or dice from there. That's it!