It depends on what you are doing. Assuming you are writing, you want to do what sounds best for the song. According to music theory, certain chords always follow others, such as a V chord is supposed to resolve to a I chord and so on. You can also use seven chords and inversions to mix things up. If you where to ask a more specific question, I might be able to give a better answer.
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i have a lot of sheet music
i learned from piano in a flash
to play root and fifth
and then from one of the dummie books play r 5th r
so most of my playing has that lullaby sound
i like it but i want more
One of the key things to learn would be how to do inversions. They are very helpful because you can switch chords without moving your hand very much. For example, say you are playing a root C major chord: CEG. You want to move to a G chord, but you really don't have the time to reposition your hand on a root position G chord: GBD. Instead, you could play a first inversion of a G chord: BDG. This is right beside your C chord. The trick is to learn to be able to do this while playing through a piece without stopping.
What level are you at playing the piano?
Chords are really just groups of keys that work well together. Rhythmically and how they are played (voicings, inversions, appegiation, and changes to flow into the next chord and so much more) are cool things to discover while playing or experimenting. Listen to a lot of music and try to figure out things by playing by ear.
i play right hand melody
and for the left chords i play root and fifth
or root 5th and another note
some more pieces went through
with a teacher years ago
There are limitless possibilities you can do with chords. There are so many of them - and so many of them work well with each other. Any number of chord progressions can be transposed into any key - pick some you like and experiment.
Once you have the chords the melody is easy :D