An example of mounting incorrectly:
Mounting this way pulls the saddle out of place and causes all the riders weight to push against it. It pulls the horses skin, puts excessive pressure on the withers, and can even cause damage to the spine.
To reduce the risk, mount by placing the left hand on the lower neck and the right hand either on the pommel, or holding the panel on the opposite side. Place the left foot into the stirrup and use the right leg as a spring, pull with your left arm, using it to help prevent pushing into the stirrup too much and distribute the weight. This method uses all four limbs to help balance and distribute weight, making it easier on the horse, the rider and even the tack.
Here the rider is mounting correctly (it is difficult to see, but her right hand is reaching to the opposite side):
This method is one of the best to use for mounting from the ground, even so, I highly recommend using a mounting block. It is one of the best tools to help keep horse and rider safe while mounting. Another excellent tool is having someone hold your opposite stirrup, or getting a leg-up. If no one is able to help you, and there is no mounting block, dropping the stirrup can be helpful.
I hope this is useful.