When the cue ball hits any cushion without spin, it ideally travels at a path which is the mirror image of the line extended ahead, on the other side of the table. This was something which I learnt long back.
Now place the cue ball on the pink spot and hit any side rail exactly perpendicular, with either left or right english. You will notice that after hitting the cushion, the CB will turn towards the english put.
A golden rule, which will help you make the cue ball travel multiple rails with ease. With sidespin, the cue ball will turn the most after hitting the rail when it is perpendicular to it, and least when it is almost parallel to it. Check out the path it travels at different angles, speeds, and spins. Also check out the article on running english and reverse english at the following link.
For other techniques, you can check out the following web page
Another thing which you can learn to master the cue ball trajectory along multiple rails is the diamond system. Check it out at the following links.
There is no effect of top or bottom spins when the cue ball hits a cushion.