I'm fairly new, although I should be better than I am...
I'm just wondering about Pull offs...

My pull offs don't sound right at all when I do them using any fingers but my first two. First I just play the 3rd note and let go and it makes no sound (See Fig. 1). So I try pulling the note up with me, like people and common sense tell me too. I do that but I end up pushing the string (Fig. 1) towards the B string. How do I do it correctly?

I understand it takes a lot of practice, but I want to make sure I learn these things the right way.

Figure 1

e: --------5-p-4-------5-p-4--------
B: ------------(hitting B string)----
You have to hold down the string fairly tightly with the lower note, in your example, the 4th fret. If you keep the finger on the 4th fret strong, you just need to work on a quick, fast, and smooth flick from your other finger's. It's mainly strength and practice to get the right technique. Youtube actually has a lot of helpful videos on this kind of thing
pull up? i always pull down.

it may take more finger strength.
and you may be letting your finger (the one playing the 4th fret) come slightly off the string when you pull off with the one adjacent too it, because it isnt that strong yet, therefore muting it, and no sound.
Ibanez S520ex
Epiphone G-400
Roland Microcube
Alvarez MC90
I just push down hard before I pull off and that works great for me. I don't know for anyone else though, just practice it and you'll get used to it.
On the eight day we spoke back...

let there be sound.