Alternate Picking

So you're probably wondering how players like Paul Gilbert, Joe Satriani, Steve Vai or Michael Angelo Batio play so fast and so clean. Super speed is achieved with a simple method of playing as many notes as possible with the smallest amount of effort. Alternate picking (up and down) is the key to success. 

So pick up a pick and hold it between your index finger and your thumb. Some players prefer to hold it differently so if you feel more comfortable holding your pick a different way, go ahead, but if you're not very experienced and not used to anything, do it the normal way. Rest the heel of your palm on the strings to mute them. The more pressure you apply the tougher you will sound. Less pressure will allow the strings to ring.

 So now that you know what you're doing, lets try some exercises. They're not meant to sound good, just improve your technique. You can play them where ever on the neck. Here are some very basic ones:

0-1-0-2-0-3-0-1-0-2-0-3-0-1-0-2-0-3-

-7-5------7-5------7-5------7-5-----------------
------7-5------7-5------7-5------7-5----------

-0-0-0-0-1-1-1-1-2-2-2-2-3-3-3-3-4-4-4-4-5-5-5-5-

You can also learn thunderstruck which requires you to pick alternately.

A very effective way to improve your picking is practicing it with scales. It will make you play faster and smoother. Once you get used to it and it becomes a habit your life will become much easier. 

Always use alternate picking, no matter what you are playing. When i was learning my guitar teacher always told me to do it, but i wasn't too keen and didn't really make an effort to practice it, but overtime I got the hang of it and realized how useful it is.