When to change chords is a little different. Like I said before, keep listening to the song you're trying to play until you know it really well. Then listen to it some more.
Personally, I like to keep things simple. I rely a lot on the rhythm of the songs I play because I either play rhythm in a group or I sing while I play. Strum patterns (and more recently picking patterns) will almost always govern my chord changes. Since chord changes almost always happen in a predictable manner, I try to find patterns that compliment the song which can be timed so the chord changes occur organically. Strum patterns can almost always be used to pace your chord changes. Most songs can be played with different strum patterns that will more or less work, but the more strum patterns you know, the more likely you are to find one that fits the song and accommodates natural, fluid chord changes.
What do I mean by that...? Okay, quick example: Angel in Blue by J. Geils Band: The rotation is C, G, Am, F, C for the verses. The chord changes occur on the last word of each verse. So, as you play it the chord changes look something like this:
(Tacet)We met in a (C)bar
Out on Chesapeake (G)Bay
With her white satin (AM)boots
And her blouse red (F)lame'
A table top (C)dancer
She would smile on (G)cue
Oh the lips of an (AM)angel (F)
Angel in (C)blue.
I play this song two ways. I'll probably figure out other ways to play it in the future because I tend to learn songs that I want to play and I play this one a lot. You could do a pretty good version of this if you did the chord changes as I have them notated before the word, but ideally they should occur right at the first sound of the word where the chord change takes place. Playing it over and over again is the only way I know of to get the timing just right.
The first way I learned to play it is with a DDUUDU strum pattern. Each note gets 2 repetitions until "Oh the lips of an (AM)angel (F)", then the AM and the F get one repetition of the DDUUDU pattern. Once you have the meter of the song in your head, you simply adjust the DDUUDU pattern to the speed of the song, and the changes will just fall into place. One problem I have with this version is that I can never come back to the 3rd verse singing in tune after the bridge. But, the song also has a solo after the 3rd verse. So I adapted it to play the solo after the bridge, which allows me to come back into the 3rd verse singing in tune. The song structure makes that sound funny though, so now I play it with the bridge and solo AFTER the 3rd verse when I play it this way.
The second way I play the song is with a picking pattern that gets 8 repetitions then 4 and 4 for "Oh the lips of an (AM)angel (F)". Again, the timing of the pattern makes the chord changes pretty natural. It also changes the mood of the song from sad & soulful to downright depressing...
Sometimes you have to just say "To Hell" with what sounds right and play what you can work with. Recently I posted a Blue Oyster Cult song that I basically had 3 choices on. I could A. Play the song wrong but as close to right as I could manage while I sang the lyrics . B. Play the song correctly without singing the lyrics. Or C. Have a psychotic episode trying to play the song correctly while singing. I opted for A., because I only had a week to work with the song, and it kinda needed the lyrics to make sense. Since I only learn songs I love to play though, there's a pretty good chance that I'll pick it up again at some point and have an "AHA!" moment and figure out a way to play the song a little better.
This is a pretty basic example of how I go about figuring out the timing on chord changes. On a somewhat related note, when I play songs with multiple strum patterns, I break down the individual parts of the song and practice the sections separately, then go back and figure out how to make it all work together. One song I play frequently has 3 distinctly different strum patterns (UDDD for the intro, DDDD, and DDUUDU) and each strum pattern makes the chord changes fall into place while I sing that section of the song.
Anyway, this post turned out considerably longer than I intended it to be. Sorry about that. I hope it helps. Your mileage may vary...