As linked by magicninja (thanks!), my modes tutorial will show you how all the diatonic modes fit together. But that only shows you where the notes are. Next you will need to know when and how to use them.

The short answer is: be aware of the chords you are playing over and use the right scale or modes to target or emphasize chord tones.

My tutorials on blues soloing show a little of this:
http://www.guitartricks.com/tutorial.php?input=217
http://www.guitartricks.com/tutorial.php?input=232
http://www.guitartricks.com/tutorial.php?input=244

I've been working on a "general guide" to improv and melodic playing over chords, but haven't finished it yet. So until then ... here's a C&P from an earlier post on the topic.

Write out all the notes in all the chords and see if you can build a scale.

To use your example: Am-F-G-C.

A minor: a, c, e
F major: f, a, c
G major: g, b, d
C major: c, e, g

Alphabetically: a, b, c, d, e, f, g, a
or: c, d, e, f, g, a, b, c

The A minor scale or the C major scale. Next, be aware of what chord is happening at any given time during the progression in order to "target" or "approach" playing over that chord with notes work with that chord.

When the A minor chord is happening play the C major scale but emphasize the notes a, c, and e (the notes of the A minor chord). To do this play those notes on the strong beats (1 and 3) or start and/or end licks on those notes. You can use all the notes of the C major scale. Just emphasize the chord tones of the chord that is currently happening. When the chord progression moves to the next chord, then change your emphasizing to reflect that next chord.

Avoiding the chord tones is a useful technique in it's own right. It is frequently how people learn to play "outside" or jazzy sounding things. But I always recommend learning to play with this chord tone approach so you understand how music works before you decide to "step outside of the box".

If the notes of all the chords do not all fit in one scale then look for a major or minor scale that contains most of them. Then look for the chord(s) that make for the exception. This is frequently a modulation chord.

Example:
A minor: a, c, e
F minor: f, a-flat, c
G major: g, b, d
C major: c, e, g

Alphabetically: a-flat, a, b, c, d, e, f, g, a-flat
or remove the a-flat and you have: c, d, e, f, g, a, b, c

Again you have the A minor scale or the C major scale. This will work fine for the A minor, G major and C major chords. However when the F minor happens you will want to alter the scale to reflect this:

Alphabetically: a-flat, b, c, d, e, f, g, a-flat
or: c, d, e, f, g, a-flat, b, c

The C major scale with an a-flat instead of an a as the sixth scale tone. So use that altered scale when the F minor happens and emphasize the notes f, a-flat, c.

Try that first. Later you can try more advanced soloing techniques. Like ...

You can also play notes from other chords and scales that voice lead (or refer) to the chords that are coming up in the progression. For example, you can play the notes from a G minor chord, then a C7 chord while the A minor chord is happening because those chords are the ii-V7 (two-five) of F major/minor chord.

Hope this helps. Good luck and happy playing.