These actions are all intended to be for general use - they may require specific equipment or circumstances, but they ought to be usable by any character. The intent is to broaden the in-combat options, especially of the martial and skill-focused characters, by supplying ready-made action mechanics and descriptions for normal fantasy tropes.
These first few actions are described in the DM's guide
If one creature wants to jump onto another creature, it can do so by grappling. A Small or Medium creature has little chance of making a successful grapple against a Huge or Gargantuan creature, however, unless magic has granted the grappler supernatural might.
As an alternative, a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb. After making any ability checks necessary to get into position and onto the larger creature, the smaller creature uses its action to make a Strength (Athletics) or Dexterity (Acrobatics) check contested by the target's Dexterity (Acrobatics) check. If it wins the contest, the smaller creature successfully moves into the target creature's space and clings to its body. While in the target's space, the smaller creature moves with the target and has advantage on attack rolls against it.
The smaller creature can move around within the larger creature's space, treating the space as difficult terrain. Ther larger creature's ability to attack the smaller creature depends on the smaller creature's location, and is left to your discretion. The larger creature can dislodge the smaller creature as an action -- knocking it off, scraping it against a wall, or grabbing and throwing it -- by making a Strength (Athletics) check contested by the smaller creature's Strength (Athletics) or Dexterity (Acrobatics) check. The smaller creature chooses which ability to use.
A creature can use a weapon attack to knock a weapon or another item from a target's grasp. The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.
The attacker has disadvantage on its attack roll if the target is holding the item with two or more hands. The target has advantage on its ability check if it is larger than the attacking creature, or disadvantage if it is smaller. A creature can use a weapon attack to knock a weapon or another item from a target's grasp. The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.
The attacker has disadvantage on its attack roll if the target is holding the item with two or more hands. The target has advantage on its ability check if it is larger than the attacking creature, or disadvantage if it is smaller.
This option makes it easier for melee combatants to harry each other with opportunity attacks.
When a creature makes a melee attack, it can also mark its target. Until the end of the attacker's next turn, any opportunity attack it makes against the marked target has advantage. The opportunity attack doesn't expend the attacker's reaction, but the attacker can't make the attack if anything, such as the incapacitated condition or the shocking grasp spell, is preventing it from taking reactions. The attacker is limited to one opportunity attack per turn.
Note - I don't think this action is particularly well constructed or phrased. I'm not clear on exactly what it means, and I don't plan on playing with it.
When a creature tries to move through a hostile creature's space, the mover can try to force its way through by overrunning the hostile creature. As an action or a bonus action, the mover makes a Strength (Athletics) check contested by the hostile creature's Strength (Athletics) check. The creature attempting the overrun has advantage on this check if is larger than the hostile creature, or disadvantage if it is smaller. If the mover wins the contest, it can move through the hostile creature's space once this turn.
With this option, a creature uses the special shove attack from the Player's Handbook to force a target to the side, rather than away. The attacker has disadvantage on its Strength (Athletics) check when it does so. If that check is successful, the attacker moves the target 5 feet to a different space within its reach.
A creature can try to tumble through a hostile creature's space, ducking and weaving past the opponent. As action or a bonus action, the tumbler makes a Dexterity (Acrobatics) check contested by the hostile creature's Dexterity (Acrobatics) check. If the tumbler wins the contest, it can move through the hostile creature's space once this turn.
As an action, you can grab hold of an adjacent ally and drag them out of a dangerous situation. Move onto that character's location with them - until the end of your turn you may carry/drag them at your full movement speed; you must release them and move off of their space before ending your turn. Your motion still provokes attacks of opportunity as normal, but your ally's does not.
As an action, move up to half of your speed, and then perform one attack or shove against an adjacent enemy. If your Attack action normally only gives one attack, then perform this attack with disadvantage. (This action is especially useful to Ready)
As an action, choose one enemy; that enemy may not perform attacks of opportunity against you this turn (treat like Disengage). Immediately move up to half of your speed.
As an action, move up to half your speed in a straight line, then attempt to shove one enemy. You have advantage on the check; if you win, you knock them prone and backwards, but you fall prone as well.