Playing the arpeggio, also known as a 'broken chord', is not that difficult if you follow a proven method of procedure that has stood the test of time. You'll find this technique occurs often in many guitar lessons.
A common way to perform an arpeggio is to begin with the thumb and then the fingers (used in succession from index to ring finger). It can have many different finger combinations.
Indeed, it is one of the more frequently used items in the 'finger-style guitar arsenal'.
Mauro Giuliani was certainly convinced of their practical use back in the 18th and 19th centuries.
He wrote 120 of them using just 2 chords, namely, C and G7. In his excellent resource, Pumping Nylon for the classical guitar, Scott Tennant says of these...
"This group of studies is the best and most comprehensive collection of these formulas I have seen."
Indeed, Giuliani himself said...
"If one could play all of these studies well, one could successfully play anything I ever wrote."
To add weight to this opinion I quote the famous guitar pedagogue, Frederick M. Noad, who said...
"They serve to develop a balanced and even touch in the fingers of the right hand."
Mostly, it is played with free stroke and they give a rippling effect by playing notes in succession rather than in 'block harmony'.
When I'm teaching students I like to get them to imagine a chord from the bass upwards in block harmony being pulled sideways. That is, stretching the chord out from left to right across the page from bottom to top.
This has the effect of making them see a clearer distinction between a broken chord and a block chord. I even get them to play these two types of chords one after the other to reinforce the difference.
That's when the "aha!" factor comes into effect. It is easy to do with a C chord if your student is indeed able to finger chords correctly.
Here is a graphic representation of what I get my student to play after he/she has mentally practised 'stretching' the chord...
Once you get used to playing this technique it is wise to play several times backward and forward or up and down if you like.
This creates a continuous cycle and helps to create if practised slowly at first, the "balanced and even touch" of which Fred Noad was talking.
My advice would be to get hold of the Giuliani studies with the arpeggio section and make them part of your regular practice routine. I can definitely vouch for them as it improved my playing ten-fold when I began them back in the dark, dim past.
Was it that long ago? Yikes!
Seriously though, perfecting this technique is to your guitar playing as what eating vegetables are for the health of your body...VITAL!
It doesn't matter what style of guitar you play. We can all benefit from a little finger style guitar that involves some some of these guitar techniques.
Here's a little video to highlight this technique...
To learn more about the arpeggio go here...