Trim the fingernails on your picking hand: it is the pads of your fingers that will be doing the work. As a beginner getting ready to start fingerpicking, 'anchor' your thumb by resting it on one of the pick-ups before you start to play. Crook your fingers just slightly -- avoid trying to play with a straight hand or curled-in fingers.
The action is to run your finger over a string, pulling it toward the string above. Start by picking one string upward with your index finger, then alternate picking the same string with the index and then the middle finger. This will give you the ability to play faster patterns than picking with a single finger. Next, alternate between hitting the second (A) string with your index finger, then the third (D) string with the middle finger. Then start to fret the strings and play a bassline, alternating between picking with your middle and index fingers. Do not worry about speed at first, play very slowly while you become accustomed to the technique. Develop accuracy first. Speed will follow with practice.
As you gain confidence at basic picking, you will be able to use a third or even fourth finger to pick more quickly and in more complex patterns. Another way to speed up your technique is to lift your thumb from the pick-up and, instead, rest it on the E string, allowing it to float free if you need to pick that string. The most important thing is to master the basics, then experiment to find the technique that suits your playing style the best.
Slap bass is a finger technique that provides a sharp, twanging sound, most famously used by funk musicians. Slap bass combines a mixture of "slapping" and "popping". Slapping is done by hitting the string with the thumb and allowing it to bounce away. Popping involves digging a finger underneath a string and pulling it away from the body of the bass: in normal fingerpicking, the finger plays over the top of the string. A good way to start practicing a slap and pop combination is to slap a particular note, for example E, then pop the same note an octave higher. Once you have got this going, slide up and down the fretboard to sound different octaves, gradually increasing your pace.