The autoharp requires an electronic tuner to get tuned. Nothing else really makes sense in this day and age.
There are two ways of holding the autoharp.
You can simply strum across the autoharp with a flatpick. You can even use cross-picking or lots of other ways to hit various portions of the harp, but it requires a lot of arm movement. Most people prefer fingerpicking it. You wear a thumbpick and one or more fingerpicks and generally strum by squeezing the fingers and thumbs together, brushing them toward each across the strings, then lifting them when you spread them apart for the next strum.
You can also alternate: Thumb-Fingers to get a bass-chord sound. Basically, all you need to do is get a regular beat going with your plucking hand and just press the chords in the correct order. There are also special autoharp fingerpicks that let you brush your fingers in either direction across the strings. These provide even more possibilities for neat sounds.
The autoharp is setup to play chords already. Whatever chords are listed on the bars are the only ones you can play. Autoharps generally have 15 or 21 bars (chords). You can make your own fairly easily, but you still have to give up some other chord to do so.
For doing the I,IV,V method I've outlined at this site, choose the right chords. F, Bb and C are on most autoharps. Look around for other three chord combinations on your autoharp and you may begin to see patterns.