If you identify the notes of all chords being used, you can build the right scale and discover the key signature. So, let's look at this chord progression over which I want to improvise. Write out all the notes in all the chords and see if you can build a scale. Suppose these are our chords: C major, A minor, F major, G major. Take those and write out all the notes those chords contain:

C major: c, e, g

A minor: a, c, e

F major: f, a, c

G major: g, b, d

Now put them in alphabetical order: a, b, c, d, e, f, g, a.

Notice that is an A minor scale, or written with the c first, a C major scale: c, d, e, f, g, a, b, c. This is essentially what a "key" is. What "key a song is in" is which major (or minor) scale all or most of the notes in the song come from.

Now you know what notes you can use to improvise. The next step is "What do you do with them?"