If you haven't read What Are Little Chords Made Of  I suggest you do that before going through this primer.  It covers some basics that are good to know.
Now here's where it gets scary... bar chords! Ha! Ha! Ha!  Umm... you see the red line which just happens to extend over every string, that's your pointing finger, well, I hope you point with that finger.  Let's just say the finger next to the thumb. :)  This is called a bar chord and frankly unless you've got 6 fingers and a thumb these must be learned.  So anyway, your index finger goes all across the fretboard and you do the E minor fingering 2 frets down and all of a sudden it becomes no other than F sharp minor.

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Now if you want to do an altered A minor do the E minor fingering on the 5'th fret barred.

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B minor is the same thing on the seventh.

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In fact it doesn't take much imagination to guess C minor.  It's the same except on the 8'th fret. And it just keeps going like that.  In fact you can use this on any chord and simply bar it.  It's called theory and it works.
All right so using theory what do think this chord is?

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Wrong! It's B.  Why?  Because it's the E fingering on the 7'th fret.  Anyhow mess around with it and if you play bar chords 'till your fingers bleed a couple time you'll have no trouble with them at all.

You can also do bar chords with the A and Am fingering.  Here is B.

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And here is Cm

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Here is a barred D

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Warning!!!
Bar chords aren't easy at first and you may experience finger cramps and great stuff like that at first, but trust me: it's worth it.