Learn your place. With a solo, there is a definite point when you start and another for when you stop. In between, you use the harmonica to express how you feel. With rhythm, however, there are no set rules about starting and stopping, nor for what you play in between. Instead of playing what you feel, you help someone else play what they feel. Instead of adding feeling, you add support and are one of several contributing to an overall sound.
Play during pauses. When a singer, or sometimes soloist pauses for a few beats, play a simple fill. Often you can compliment by playing a riff similar to what the singer has just made in call and response fashion. There are exceptions, but usually the simpler the fill the better.
Anticipate the chord changes. Play fills that takes the music from one chord to the next. You'll hear this a lot with Chicago-style blues players using fills to add gradual tension from the I to the V chords.
In rhythm playing, you rarely want to sound busy, remember, you are only there at that point to compliment someone else, not show off your skills. It is NOT about the harp, it is about contributing to an overall sound.
Lower notes typically work better than extremely high ones as they blend in better. Make sure, very sure, that you are playing in time.
Most blues songs have the same chord progression. That's why blues players have such a knack for jumping in and playing wonderful solos, even if they have never heard the song before.
Here's the standard 12-bar progression, with chords for each in the key of G. In G, the G is the I chord, the C is the IV chord and the D is the V chord. The progression is the same for any key, only the chords are different
Here is a common 12-bar blues progression. Each number is a measure, which equals four beats, followed by the chord of that measure.
(1) G (2) G (3) G (4) G (5) C (6) C (7) G (8) G (9) D (10) C (11) G (12) G
All these chords can be found on the harmonica and you can back up a blues song playing nothing but chords. At first, simply draw the length of one measure, stop quickly and draw again for the next. Later, try slapping your tongue against the roof of your mouth to cut off air to make short notes for each beat. After you've mastered that, try varying your rhythm by accenting the 2 and 4 beats.
On a C harmonica, you can play the G chord with 2,3 and 4 draw, the C chord with any three blow notes and the D chord (it will actually be a D minor, but it's OK) is 4,5 and 6 draw.