The first technique taught in almost all Jiu Jitsu classes is the simple Upa or bump and roll technique to escape from the bottom of the mount. There are several reasons that this is the case. Much of Jiu Jitsu can be difficult to understand for a brand new practitioner. Shrimping, guard, half guard, spider guard, sweeps, guard passes can take a while to understand for a newbie, but being caught underneath an opponent mounted on top of you, it is frighteningly easy to understand why you would need to escape as soon as possible. Your opponent has any number of ways to attack you from the mount. Punches, headbutts, elbows, chokes, smothers, and armlocks are all readily available to him while your offense is basically non existent from the bottom. It is of utmost importance that when training you develop the ability to recognize the significance of each position and what is available offensively and defensively for both yourself and your opponent.
Your only option when caught mounted by an opponent is to escape. Ideally you will be able to trap and arm and leg and bump your hips up off the ground and roll over on top of your opponent. This is the preferred method of escape in all of the grappling arts including BJJ, but BJJ also offers us the ability to escape back to guard or half guard where we can utilize our legs in order to gain control, sweep, or submit our opponent. In jiu jitsu, you will most likely find that against more highly skilled opponents, you will more often than not be getting back to guard rather than simply bumping your opponent off of you.
Escaping bad positions is good but not good enough. You will also want to develop the ability to seamlessly transition from defending and escaping to attacking and sweeping or submitting. There should be almost no space between your defensive escapes and your offensive attacks. One of the best times to launch an attack it immediately after an escape when your opponents focus is most likely centered on preventing your escape rather than defending themselves from an attack. You will often find an opponent off balance or over extended after you escape which will allow you to possibly catch a quick submission or reverse position and get on top.
In this video from the Hellfish Mixed Martial Arts YouTube channel, we cover how to escape the mount and transition immediately into a simple sweep from the half guard.