If you have had the experience of playing with other musicians, playing a solo mandolin can sometimes sound a little pale by comparison. Playing chord melody can be the perfect solution for that. Chord melody is used most often when playing jazz or blues mandolin, but can be impressive when playing classical music or solo breaks in bluegrass music too.
Start by learning the basic melody, using these audio files for Jerome Kern's "Pennies From Heaven". This is a jazz standard from the Great American Songbook, and is not played in strict time. Instead of dividing a quarter note exactly in half to play an eighth note (like you would in bluegrass or Irish music), you will play the second eighth note a little late, about 2/3 of the way through the beat. This is called a "swing" and, from a practical standpoint, no one ever does that math when they're playing swing. Instead, it's more of a bouncy feel - although you always have to keep the correct timing with your quarter notes. Here is what it sounds like without the "swing".
You can hear that the song sounds sterile and dull without the "swing", so use these audio files when you're practicing:
Note that measures 23 and 29 have lines with a "3" above them. These are triplets and, when you see that, it means you must fit three notes in where you would normally play two - with each note having the same value. Triplets are used in songwriting when the composer is trying to make the music fit with the lyrics - in measure 29, those triplets go with these lyrics: "pennies from heaven for" and the long notes in the next two measures go with "you and me". If you encounter triplets in another song, you can also say the word "strawberry" in your head - it has three syllables and will match the rhythm of the triplet perfectly.
Once you get the basic melody down, try to work some chord melody into the song. Some spots are easier than others - skip the hard ones to start, and try the easy ones first. The first three notes, for example, are pretty easy. You'll use your middle finger on your "A" string, your index finger on your "D" string, and your open "G" string to make those chords. The fourth note of that measure, though, isn't that easy - you have to use your index finger on the second fret of both your "D" and "A" string, in order to make that combination. (That's called a barre chord!) When you're starting out, it will be difficult to get that barre chord with accurate timing, so skip the chord for now and just play the melody note - the fifth fret on the "A" string.
The third measure also has some chords that can be difficult - in order to play them, you have to use your pinky on the "G" string. It's easier if you learn these kinds of chords in steps. Start by trying to play only the top two notes of the chord - in the third measure, that's your open "A" string, along with your middle finger on the third fret of the "D" string. Once you can play the two-finger chords in the correct time, try to add a third finger to your chord. Note, the tablature is set up so that, if you play the full chord, you won't ever use your "E" string. This is because you'd have an open string somewhere, that isn't supposed to be part of your chord! But if you want to play jazz, blues or bluegrass, you should get used to using your pinky.
Chord melody is difficult to master, but it can add a wonderful sound to your playing. Start with the easier combinations, and work your way up to the harder ones.
And, there is a wonderful version of this available on YouTube, by jazz master Don Stiernberg!