The technique of playing slap-style or thumb-style on a bass guitar is to strike a low string with the side of your thumb, giving it a percussive sound (a sharp attack and decay of the note, like a drum), and then to snap (or pop) a high string with your index finger. Here's how you do it:
Make a light fist with your right hand.
Lift your thumb away from your fist as though you were hitchhiking.
Loosen up on your index finger and create a hook.
Your index finger should look like it's pulling the trigger of a gun.
Rest your forearm on the body of the bass so your right hand hovers above the strings.
With a sharp twist of your wrist, flick your thumb against one of the low strings, striking it at the very end of the fingerboard.
This flick creates the slap sound. You need a lot of wrist movement for this style.
Hook your index finger under a high string, and with an opposing twist of your wrist, pull the string away from the fingerboard, and then let it snap against the frets.
Make sure your thumb continues past the string and onto the fingerboard so the string is free to vibrate and the note rings.
Don't pull too hard on the high string, or you may break it. Only a small amount of force is required.