#1
i am used to playing led zeppelin guns n roses and those type of bands, but now i wanna try some metallica and zakk wylde, they basically just pick extremely fast and dont use hammer ons.

so i was wondering what i could do to improve the speed of my right hand picking?
#2
I dont know if im doing it right, but im just trying to get the feel of both up and down strumming of the strings.
Then gradually i will get the feel for the strings, and i shall be able to pick notes faster, as that should allow me pick two notes on one string without a hammer-on.

Im most likely doing it wrong, but any method is better than no method.
So wait for other opinions or google around
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#3
Strictly speaking nothing.

Speed is governed by a load of other things but it's not something you can work on directly...but you can of course work on the things that limit how fast you can play, namely

Accuracy - if you can't hit the right notes at a slow speed you'll never be able to do it quickly
Synchronisation - you have to get both hands working together and in time, if you can't do that then you're trying to play too fast and need to slow everything down.
Timing - kind of ties accuracy and synchronisation together, you need to be able to play in time, and if you're inaccurate or both hands are out of synch you can't do that
Stamina - if your hands get tired your playing will invariable go to pieces
Knowledge - if you don't know your way around the fretboard, don't know your chords and don't know what scales to use that's going to slow you down...how fast you can think is just as important as your physical skills

Work on those things and speed will take care of itself.
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#4
Practice your alternate picking with scales, modes, rhythm chops but use this: