The following chord chart shows most of the commonly used altered chords. There are always more possibilities, so experiment with formulas and transcribe Jazz piano parts and you will never stop learning new chords. The study of chords and harmony is a lifelong process. The more creative you can be with it, the more fun you will have.
In altered chords, the notes to be altered are always written as part of the chord name, enabling you to construct the chord. For example, a Cm7#5b9 (not listed here) is a Cm7 chord with the fifth sharpened (#5) and the ninth flattened (b9). When you are working out a suitable shape for this chord, remember that the root note and/or the fifth note may be omitted.
Another type of alteration occurs by the use of slash chords, e.g.:
Example 1: G/F# bass This indicates that a G chord is played, but using an F# note in the bass. Together this adds up to a G major seventh chord (Gmaj7).
Example 2:E/C bass This indicates an E chord with a C bass note. Together this adds up to a C major seven sharp 5 chord (Cmaj7#5).
Usually the word "bass" will not be written (i.e., the symbol will be just E/C), but the same meaning is implied. Most slash chords add up to another chord type.