The Spider is, I think, the ultimate alternate cross string picking exercise. Prepare to become arachnophobic because this is a nasty little alternate picking exercise. It is very difficult and will take a lot of practise to get smooth and fast, even for a fairly experienced player. It works the alternate picking to the max making it cross strings and jump about in many combinations. A real helper if you need to develop your picking for playing arpeggios too!
This exercise is NOT for beginners. I think it is a great essential exercise but wait until you have been playing your major scales and need to start pushing your technique. It is a hard exercise, but if it just seems impossible, then maybe give it a rest and come back to it later.
Make sure you start off very slowly, there is a very obvious pattern to the notes, I think of it like a diagonal line moving across the fingerboard. It helps to think that some of the fingers are starting on invisible strings off the fingerboard, and the “line” moves across one string at a time. Follow the TAB in Ex.1 carefully and get it correct from the start, try not to learn it the wrong way. Get the fretting hand fingering perfect and to memory before you think about the alternate picking aspect of the exercise.
Once you have the pattern down really focus on the picking, you should not have to look at your left hand, so you should devote all your attention to your picking hand. Try to make the pick move as little as possible.
Keep to a tempo where you can play in time, without stumbling, tripping up, or slowing down for the "harder bits".
Once you can play it at a consistent (slow) tempo, start to use a metronome, but do not be in a hurry to start pushing the speed up. Get very comfortable with the tempo before you even think about speeding up. This is important because practicing the wrong movement is worse than not practising at all!
Make sure that you alternate your picking, starting each time with a down pick. The last note in the sequence should be an up pick.
A good trick once you get the basic idea is to start down at the 1st fret and work your way from the thinnest string, down to the thickest. Then move up one fret and now go from the thickest to the thinnest, then up another fret and so on… You will find that it feels different once you start moving it around the neck.
See Ex.2 to see how to move it up the neck, but only the first three frets of the exercise are shown, you should continue up the neck. It gets very hard past the 12th fret, so only get up that far when you are comfortable with the exercise up to that point, or if you do a lot of playing up the “dusty end” ;).
Those that are really adventurous might like to try starting with an up pick, but save that until you have mastered the original exercise. It is quite a lot harder and somewhat unnatural as we usually use a down pick on the beat.
Another alternative is to play the “diagonal” the other way, starting with the 4th finger. This can be good for them, but adds no benefit to the picking because it remains the same as the exercise shown. I don't recommend this version anymore (it used to be part of the original exercise) - except as a fretting hand exercise!
Good luck, you'll need it :)