Determining chords can be a slow, tedious process and I do not know of any easy way to do it. I have music that does not have chords indicated above the staff. I have successfully determined the correct chords. Here is how I approach the problem.
First, I note the key signature of the song. This obviously tells me what chords are likely to be encountered. For example, a song in the key of Eb would contain chords whose roots are Eb,F,G,Ab,Bb,C, and D. Then I begin by looking at the first bass note. The bass note will generally indicate the chord name. Then I look at the notes stacked above the bass note. So for example, if the bass note is Eb and the notes above it are G,Bb,C, I know the chord is Eb6. If the top note is a D, then the chord is Ebmaj7. If the notes above are G,Bb,Db it is Eb7. If the notes above are G,A,Db, then the chord is Eb7b5 and so on.
You may encounter diminished chords. It is important to remember that there are two diminished chords for every key note. Thus, in the case of Eb, you have an Ebdim chord and an Eb#dim (more conventionally known as Fdim)- every keybote has a diminished chord and a #diminished chord.
That is the process I use. Perhaps others have a different approach and can post their thoughts.
A long time ago I wrote a piece entitled "Introduction to Chord Voicings". It was sent to all forum members by Bebop. If you study it, it will help you understand chord formations/alterations. It is available for download on Bill Norrie's websight if you are interested.
Hope this helps. Take care, Jack and good luck.