You need to learn how to understand song structure/pattern. The order of the chords/pattern of a song is called the "Chord Progression". When you strum chords on a guitar, you're playing songs at its basic level: the chord progression. All songs are played in a specific key (playing "in" F, in G, in C etc.). For each key there are three basic chords (really more but just for starters we'll focus on three) that you can play together.
There's a "starter" chord, the one you'll usually begin and end on. I call it the "first" chord or 1 : the corresponding chord for a key (If you're playing in C, then the first chord is C)
A second chord (2). Each key has a specific correct second chord. In C its F. There's charts and stuff to help you remember, and over time you'll memorize which chords are for which key
A third chord (3) is usually the one you go towards the end of musical phrase, just before ending on the 1 chord. In the key of C this chord is G.
So a pretty common chord progression would be something like,
"1.2.1.3.1"
or
"C.F.C.G.C"
Of course there are always ways to switch things up and those three chords can play different roles in different orders, the important thing is that for each key there's three main chords that "go" together. Here's a few keys just for reference....
In key of G: 1=G
2=C
3= d
In key of C: 1=C
2=F
3=G
In key of F: 1= F
2=Bflat
3=C
Try looking up "nashville numbers", its a common system. I think the chords are labelled with different numbers but its the same concept. There's probably even a thread somewhere on Chordie about it.
Once you begin to understand the pattern of music, you'll start to recognize it in songs and it'll make it much easier to pick up on new tunes. You'd be surprised how many songs, when stripped down to their most basic level have super similar chord progressions. When you recognize a chord progression, you won't have to work as hard to memorize what chords go in what order! You'll be able to look and see that you're playing in a key, know what 3 chords are probably going to be there, and even what order they're most likely to fall in.
Best of luck!
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