I have all of my music on an external hard drive to save space on my MacBook Air. Is there a way to use iTunes Match so that I can play music from my external on my iPhone and iPad?
No.
iTunes Match will only stream from 'cloud' servers... if you want to play what's in your local iTunes library on another local device, you need to use AirPlay.
I think what she is asking is how she initially matches her library. Since it's on an external and won't all fit on her Macbook Air.
I'm assuming some of the music is purchased from iTunes and some is not.
This is a question I was interested in knowing the answer too as well. I'd like to clear off some space on my hard drive but not if it's going to pull them from Match.
Not quite. As Karen said, it downloads each song to your i-devices as it plays them. I bought it thinking I could stream to my iPad mini and I was wrong. Wasted $25. I just uploaded them to Google Play so I could stream to my iPad. And that was free.
And to answer Heatmel's question, I don't think it can be done from a external HD. Or at least not that I'm aware of.