Being able to play the chords to songs by memory is liberating and allows you to put a whole lot more self-expression into performances. However, getting to that point is something people will go to great lengths to avoid! A motivating factor, an upcoming performance for example, and some of these methods can help
Start off with simple songs that you know well enough to sing along to, and with three or maybe four chords maximum. Have a look at the pattern or progression of chords. Writing out just the chord names on a sheet of paper, in the order they occur in the song, can shine a light on this.
Chord progressions can make more sense if you understand a bit about key signatures and chords. For example, the I, IV, V and vi chords are commonly found in simple progressions. In the key of C those chords are C, F, G and Am, and/or their seventh versions. In the key of G they are G, C, D and Em. Look it up to find out more (or purchase Friendly Music Theory from this site!)
Stand up and play (to no-one at first), with the chord/lyric sheet at glancing distance but not straight in front of your face. Try and remember two or three chords at a time before glancing back at the sheet and looking ahead at the next two or three.
If you are a visual learning-type person, think about the chord shapes your hand has to move to and from, or visualise what chord appears on the sheet next to/above the lyrics you are singing.
If you're playing in the same key as a version of the song on YouTube or your record collection, try playing along.
Finally, don't be hard on yourself if it's not going to plan or taking longer than you expected. Tailor the learning to yourself, take it slowly and work on small portions of the song - a verse or even a line.