Minor chords are said to have a "sadder" quality than major chords. Sometimes, the "rules" of music theory require minor chords to be used for certain chords within a specific key; however, those rules are beyond the scope of the learning level of these lessons. For our purposes, you need to be able to apply a minor chord when a particular song tells you to, not know why it's telling you to.
As the Circle of 5ths & 4ths diagram [PDF] shows you, the difference between minor and major chords is the third. To review from the major chords lesson, a simple chord consists of the root, fifth, and third. If you recall, for major chords, the third is "sharpened." For minor chords, the third is natural. If I don't use the Circle of 5ths diagram, I can count up five notes starting from the root. For an E chord, that means E-F-G-A-B. An Emaj has a G# for the third; Em has a G. That's the only structural difference between major and minor.
This structural difference is clear when looking at the major and minor chord diagrams. Compare an Emaj on the Major Open Chords diagram [PDF] with the Em on the Minor Open Chords diagram [PDF]. You'll see the Emaj has a fretted G# and Em an open G string. Studying the other chords of both the open and barre varieties reveals one note shifts. Sometimes, like with Gm, that requires a completely different fingering to make the chord easier to play, but there's always a single note difference between the two.
Using the same regimen described for major chords, practice forming minor chords. This should be easier for you since you've developed finger strength and dexterity with major chords. Once you feel some mastery shifting between various minor chords, work in major chords and practice shifting between major and minor. (As you get good at this, you can jump ahead to the Reading tablature page if you want to start playing some simple songs. For now, don't worry about any 7th chords, just play them as minors.)