They would imitate one another, they would argue, they would present contrasting ideas etc. In musical terms, we would think about creating dialogues and duets.
In a dialogue, two or more parts would play in alternation - one part would play rhythmically more active material, while another holds a longer note or plays something in a slower note values. Then they switch roles.
In a duet, two parts would play together, mostly in similar rhythms using sweet sounding intervals of the thirds and the sixths.
In a dialogue, suspensions when two parts form a dissonant interval of the second, fourth, seventh or ninth followed by the step-wise resolution to the consonant third, sixth, or octave are also very popular.
Today's sight-reading piece is Trio Sonata No. 1 in Eb Major, BWV 525 Part I (p. 2-5) by Johann Sebastian Bach (1685-1750). In this case, there are 3 characters at play here - two in the the treble clef and one in the bass clef.
When you sight-read this piece today, don't feel pressured to play all parts together right away. If you don't feel comfortable with the trio texture, play separate parts. You will notice that each part is so musical and complete that they sound like separate musical compositions.
Remember to keep your fingers and feet in contact with the pedalboard whenever possible, play with articulate legato touch, and don't use heels in the bass part.