One of the best ways to become familiar with chords in all keys is to take a simple progression and transpose it to all of the keys. This may be slow at first, but the more you do it, the easier it gets. Here are some common progressions to learn and transpose. Remember to practice them in different ways, e.g., with either hand, both hands together and as arpeggios.
Once you have learned any basic progression, experiment with finding different ways of using it to create music. Here is another version of the same melody, this time accompanied by a bass line derived from the chords and connected with passing notes from the C major scale. There are always many different ways to play a chord progression.