Choose to play in either a major or minor key. Write down the key signature and take notes on your manuscript paper to help remember your chords. Choosing to play in either major or minor keys will not affect the progressions, but it will affect the chord values from being either major or minor.
Play a three-six-two-five-one chord progression on your instrument. In C major these chords are e minor, a minor, d minor, g dominant seven and c major. This sequence of chords is usually notated with numerals like this: iii vi ii V I. Lower case numerals are used for minor chords and capital numerals are used for major chords. In C major, these major and minor values happen naturally within the major scale. This will be true of all major scales. In minor, these chords will be e flat major, a flat major, d diminished g seven and then c minor. The numerals for the minor sequence are III, VI, ii, V i. Knowing the values is most important for learning these chord progressions, because it will help you play them comfortably in every key.
Find the common tones between the chords in your chord progression and keep them sustained throughout the chord progression on your instrument. For instance, moving from e minor to a minor, the note E is the root of the e-minor chord and it is also the fifth of the a-minor chord. Keep the E as a common tone to smoothly transition from the e-minor chord to the a-minor chord. Moving from a minor to d minor you can keep the A as a common tone. If you are using sevenths and ninths, then the C and the E from the a-minor chord can be kept and used with the d-minor chord.
Resolve your thirds and sevenths in all dominant chords correctly. In standard harmony practice this method consists of resolving the thirds in your dominant chords up a half step and the sevenths in the chord down a half step. This means that the B in your g-dominant chord will go up a half step to C and that the F will go down a half step to E. In c minor the F will go down a whole step to e flat.