This is how it was taught in my school, where it was always the first application taught.
Ward-off is to get the leading arm under the opponent's upper arm, and make forearm-to-forearm contact with that same arm with your off-arm. Rollback is used to turn the shoulder in a lock, controlling the elbow, to "drag" the opponent towards you down and to the side.
Ideally this lock is done using only the forearms, but off-hand can grip instead. The front knee of the bow step is ideally used used to control the opponent's knee and decrease their leverage.
Drag can be used to put the opponent's face into the ground, damage or dislocate the shoulder, or hyper-extend the opponent's elbow.
However, every Chinese martial arts practitioner should know the counter to this, both traditional Shaolin & internal. Essentially you unroll the shoulder into the opponent, and displace/uproot them with a shoulder push. (There is also a nasty liang yi stepping counter that controls the dragger's arms and finishes with an throat strike they can't block from that grapple.) Thus:
You let the opponent get out of the lock by drawing back, and, maintaining body-to-body contact (stickiness), make the press
" Press" is focused two-handed push with outer palm inward & inner palm outward,
where the palms are touching.
This press can be used to push an opponent with a great deal of power. The arms move only a small amount, as the power must be generated by emptying the chest, combined with a little forward waist movement.
Press can also be used as a powerful strike against the solar-plexus. Again, the extension of the arms derives from sinking the joints and emptying the chest and this cannot be over-stressed—using brute force for this technique is particularly ineffective.
Like drag, the counter to this is to rotate the body toward the presser, emptying the chest in case of strike, and to neutralize the power of the press. This body-turning makes a linear counter-strike impossible, such that the expected response is a hook punch, or, if a Chinese boxing practitioner, potentially "strike ears with fists", which is a double temple strike.
Split is used to counter the strikers arms, outward and downward in a circle, trapping the elbows, and moving forward into a push.
Tai Chi push is 99% waist. The arms should form a stable, rounded structure, and not move—all power comes from the waist, using the oppositional anchors of the ground and opponent's body.
Stickiness is essential for high-level Tai Chi technique, thus "relaxed, calm, continuous, with intent and energy". (My teacher called this developing "feeling", and, in this case we use energy to connote momentum.)
The ideal push first uproots the opponent, pushes lightly to get the opponent moving, then pushes powerfully into that motion.