Hey, there!
There are a lot of really effective mount escapes, so I'll organize my thoughts in terms of earliest (preventative) to latest (most desperate).
1. Preventing your opponent from mounting (from side control this can usually be accomplished by keeping your inside knee wedged way up between you, or leaning on the door to take that space as soon as they move).
2. Preventing your opponent from stabilizing the mount (Reverse Alcatraz is a good example, where the mounted position never truly exists for more than a splite second. If you're familar with Gracie Combatives, they teach an elbow escape on the leg which is stationary during a mount transition, so that, again, mount never truly takes place).
3. Preventing your opponent from progressing North or attacking your neck (Immediately using the George Foreman frames to keep their hips South and in range of elbow escapes or Escape From Alcatraz. This is where the bulk of my mount escapes happen, and they're almost always a) elbow escapes b) escape from alcatraz c) quarter guard recovery via heel drag d) "Suprise Trap and Roll" off of a failed elbow escape).
4. Desperation time (Some people are incredible at the Hail Mary escape, but I am not one of them. At this point, when your opponent is way North on you, your elbows are up, your arms are dead to rights, this is the time that I hit the Hail Mary straight in to leg locks. If that's failing, the next best thing is to try to wiggle North and re-establish safe arm positioning ).
Good luck, sir.