Improvising on a chord progression goes something like this....
for instance a chord progression given is C , G , D , A for example....
You could play a C7 , G5 , D7 , A5 or a Cm7 , Gsus7 , Dm7 , Asus7
If a chord last for 4 beats , you do some simple appaeggio for the 4 beats and then play the other chords...
for example you could play a C appaeggio and then a G chord then D appaeggio and lastly an A chord
Basically you can play any chord belonging to the same family as long as the chord mentioned for instance the C chord you could play a C7 , C5 , Cm7 , or Csus chord instead cause after all it still belongs to the C family and so on....
There are loads of other ways to improvise and what i'm giving you now might be only be the tip of the iceberg
