Underwater Combat
A creature without a swimming speed moves at half its walking speed, round down.
When making a melee weapon attack, a creature that doesn't have a swimming speed (either natural or granted by magic) has disadvantage on the attack roll unless the weapon is a dagger, javelin, shortsword, spear, or trident.
A ranged weapon attack automatically misses a target beyond the weapon's normal range. Even against a target within normal range, the attack roll has disadvantage unless the weapon is a crossbow, a net, or a weapon that is thrown like a javelin (including a spear, trident, or dart).
Creatures and objects that are fully immersed in water have resistance to fire damage.
Underwater Visibility
Visibility underwater depends on water clarity and the available light. Without an available light source, water clarity alone determines encounter distance or the ability to make out details of the environment.
Underwater Travel
Unless aided by magic, a character without a swimming speed can't swim indefinitely. After each hour of swimming, a character must succeed on a DC 10 Constitution saving throw or gain 1 level of exhaustion.
A creature with a swimming speed—including a character with a ring of swimming or similar magic—can swim all day without penalty and uses the normal forced march rules in the Player's Handbook, which are:
"For each additional hour of travel beyond 8 hours...each character must make a Constitution saving throw at the end of the hour. The DC is 10 + 1 for each hour past 8 hours. On a failed saving throw, a character suffers one level of exhaustion."
Deep Water
Swimming through deep water is similar to traveling at high altitudes because of the water's pressure and cold temperature.
For a creature without a swimming speed, each hour spent swimming at a depth greater than 100 feet counts as 2 hours for the purpose of determining exhaustion, and swimming for an hour at a depth greater than 200 feet counts as 4 hours.
Putting It Together With Examples/My Interpretation
Example 1: A Character With a Swimming Speed
Can travel underwater, at any depth, for up to 8 hours without issue. For each additional hour of travel beyond 8 hours, it must make a Constitution saving throw at the end of the hour.
Example 2: A Character Without a Swimming Speed
Not at depth: After each hour of swimming, the character must succeed on a DC 10 Constitution saving throw or gain 1 level of exhaustion.
At depth >200 feet:
The character must succeed DC 10 Constitution saving throw at the end of each of the first two hours,
and a DC 14 Constitution saving throw at the end of the third hour. Failing any of these saves causes the character to gain 1 level of exhaustion.