Combat Movement

In combat, characters and monsters are in constant motion, often using movement and position to gain the upper hand. On your Turn, you can move a distance up to your Speed. You can use as much or as little of your speed as you like on your turn, following the rules here.
On a square grid, you can move vertically, horizontally, or diagonally at the same rate.
Your movement can include Jumping, Climbing, and Swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However you're moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.

Breaking Up Your Move

You can break up your movement on your turn, using some of your Speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet.
Moving between Attacks
If you take an action that includes more than one weapon Attack, you can break up your Movement even further by moving between those attacks. For example, a Fighter who can make two attacks with the Extra Attack feature and who has a Speed of 25 feet could move 10 feet, make an Attack, move 15 feet, and then Attack again.
Using Different Speeds
If you have more than one Speed, such as your walking speed and a Flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new Speed. The result determines how much farther you can move. If the result is 0 or less, you can't use the new speed during the current move.
For example, if you have a speed of 30 and a flying speed of 60 because a wizard cast the Fly Spell on you, you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet more.

Moving Around Other Creatures

You can move through a non-hostile creature's space freely.
In contrast, you can move through a hostile creature's space only if the creature is at least two sizes larger or smaller than you. Remember that another creature's space is difficult Terrain for you.
Whether a creature is a friend or an enemy, you can't willingly end your move in its space.
If you leave a hostile creature's reach during your move, you provoke an Opportunity Attack.

Trampling a Creature

If a creature is Prone, you can Move through its space and trample the creature, dealing Bludgeoning Damage. This damage is based on the your size and weight -- a Medium-sized Humanoid would deal 2d6 bludgeoning damage, whereas a large Warhorse would deal 3d8 bludgeoning damage.
Tiny: N/A Small: 1d4 Medium: 2d6 Large: 3d8 Huge: 4d10 Gargantuan: 5d12

Tumbling

Whether Prone or upright, you can attempt to tumble through a hostile creature's space if you are too large to do so normally. As a Bonus Action, you make a Dexterity (Acrobatics) check Contested by the hostile creature’s Dexterity (Acrobatics) check. If you win the contest, you can move through the hostile creature’s space once before the end of your Turn. This Combat Movement does not create an Opportunity Attack.
Related articles:

• Terrain
• Moving while prone
• Creature Size and Space
• Flying Movement