When interacting with a willing creature, once during your move, you can mount a creature that is within 5 feet of you or dismount. Doing so costs an amount of movement equal to half your speed. For example, if your speed is 30 feet, you must spend 15 feet of movement to mount a horse. Therefore, you can’t mount it if you don’t have 15 feet of movement left or if your speed is 0.
If an effect moves your mount against its will while you’re on it, you must succeed on a DC 10 Dexterity saving throw or fall off the mount, landing prone in a space within 5 feet of it. If you’re knocked prone while mounted, you must make the same saving throw.
If your mount is knocked prone, you can use your reaction to dismount it as it falls and land on your feet. Otherwise, you are dismounted and fall prone in a space within 5 feet it.
If you are attempting to jump onto or climb another creature that is unwilling, this action can be accomplished 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. The larger creature's ability to attack the smaller creature depends on the smaller creature's location, and is left to the DM's 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.