How do I properly cut leafy herbs like basil?
Strips of herbs is called a chiffonade:


Stack the leaves together.
Roll the leaves into a cigar shape
Slice across them.


I typically use a chef's knife.

If I have multiple herbs, I'll wrap the smaller leaves in one of the larger ones.  (eg, basil &amp; oregano)

If you want it minced, then you should "run your knife through" the pile.  Which in expression to mean in this context to rock your knife over the pile, turn it, rock it some more ... and keep repeating until everything's the size you want it.

update : 

Even though the question clearly stated 'like basil', for other sizes/shapes of leaves, there are ways to efficiently get them into a cut up pile (possibly strips) that you can then mince finer:

For longer-leafed herbs (eg. culantro), you don't need to roll up the leaves. Just stack up what you need, hold them from the stem end, and rock/slice them.

For small leaf herbs, you're not going to get what I'd call strips.  It's more like confetti.  If you don't have a larger leaf in the recipe to wrap them in (basil, mint, sesame, or even vegetables like spinach), then you'll want to keep the leaves on the stem.

For tender stem plants (celery, parsley, etc. (except for cilantro (green coriander) -- throw that out and use culantro instead, as it doesn't taste like soap), you just hold the stem end and rock/slice your way from the top.

For woody stems, you work similarly, but slow down when you're getting close to the woody part.  Then you turn the stem so you're cutting more parallel with the stem, and cut in from one of the sides.  Roll the stem over, and continue working in from the side.  Repeat until you've gotten off all you can without cutting into the woody stem.  If there's still a lot of leaves left, break off the branches of the stems, and either work them  individually or stack them up to try to work a bit faster.  (For some plants, it's easier to break it off before you start, and work each one individually.)