One of the biggest mental challenges when confronted with a chord chart is the sight of an extended chord. The brain goes in to a frenzy. "I've only got five fingers in my right hand, they can only stretch so far. How do I play a Fmaj9 without breaking my hand?"
Easy. Don't play all the notes.
Let's look at the following progression in the key of C major: Am7 Fmaj9 C(add9)
Scary? Probably a little. Lets take it step by step. First, we'll look at the individual notes that make up those chords.
Am7: A C E G
Fmaj9: F A C E G
C(add9): C E G D
The Am7 can be comfortably reached with one hand by most players but the Fmaj9 and the C(add9) are a massive stretch. To make this as easy as possible, we're only going to play three notes of each chord in our right hand.
Our left hand is going to play the root note of each chord, while our right is going to play all of the important notes that we need to include to make sure our chords are properly represented.
By looking at the individual notes that make up each chord, we can group the chords in to inversions that makes it as easy as possible to play each chord.
Am7 A E G C (I've moved the right hand to a different inversion)
Fmaj9 F E G C
C(add9) C E G D
There's absolutely no need to put the root note of the chord in the right hand if your left hand is playing it. If we did, the Am7 would have a G and A side by side in the right hand, muddying the voicing. Even more dramatic would be the Fmaj9, with an E, F, and G all sandwiched together. Taking the root note to the left hand gives the rest of the chord the space it needs in the right hand.
Hang on - what happened to the A note in our Fmaj9 chord? Isn't that important?
Well, yes and no. The A in our F chord is important, in that we need that third to let us know whether the base of the chord is major or minor. However, our brain is magically filling in that A for us.
Why? Because the previous chord, the Am7, uses an A. In hearing that chord first, our brains have stored that harmonic information and will insert it in to any further chords whether we like it or not. Playing an Fmaj9 without an A in isolation, without any surrounding chords, the chord does lack a major or minor sound. By playing a chord nearby that has an A, our brains fill that in, and the chord sounds like it has a major base.
How much easier does that look, and feel, to play? The more practice you do with these inversions and voicings, the more comfortable you'll be to play any chord chart put in front of you. (Until you're confronted with a PROPER jazz chart. Yikes.)
Related: Chords and Their Giant Extended Families