Here we see the main acoustic guitar for the song. Although the strumming is fairly fast, the chords are mainly common guitar chords. You don't have to worry too much about getting the strumming precise in songs like this. Just get the chord changes in the right places with whichever strumming pattern feels natural to you and it will sound fine.
He uses a lot of partial strums, meaning that just certain parts of a chord are strummed. Even so, keep all your fingers in place. If you overstrum it will still sound alright.
Also, there are occasional variations on chords (adding / removing notes etc). They're all here, but don't worry about every fine detail. Get the basic chord progressions down first, and add those little touches in afterwards if you want. The whole song is here, but the following breakdowns are all you need to learn it:
Intro - Cycle twice between these 3 chords:
G major - C major - D7 sus4
Verse - The first verse is played a little differently to other verses but only because it has an extended start on the first chord. It starts with this G major chord. Add / remove the 3rd finger, as shown. Later in the song this chord is not done during the verses. It is replaced by the last G chord riff of the chorus instead. The standard verse progression then continues as normal:
G major - C major - G major - D major - C major - G major - D major - C major - G major
Chorus - The chorus is quite big, so let's break it into sections:
Part 1: Em7 - E minor - C major - G major - mute - G major
Part 2: A minor - C major - E minor - Em7
Part 3: C major - G major - C major - G major - A minor - C major
Part 4: This is a repeating riff based around a G major chord.
Solo backing - This part involves playing the verse / chorus sections again, albeit with different strumming and picking through notes. For most people, just repeating the verse / chorus chords again will be fine, but if you want to see how the Eagles played it, it's here.
Outro - Nice and easy. Just alternate between C major and G major!