Write down what part each instrument plays in the quartet (and I mean melody, harmony, continuo etc, bearing in mind they should change roles frequently) and expand that into a structure, for example, 1st violin starts with melody for seven bars on a solo, and then 2nd takes over, while 1st plays a counter melody or harmonic part, and the cello starts playing some pizz notes, for example?
Then write down the main melodic idea, and shove some chord sequences or harmonies or counter-melodies in with it. As the music gets developed, use more variations. Just keep in mind what role each part is playing in the music.