Here are some of the in-depth mechanics of the game. The first two are very important, the rest is fairly simple.
Kill Set ups

All characters in the game have something called kill set ups, this essentially guarantees a stock depending on the situation. By using a move that pops the opponent up perfectly for a killing follow up is what we call a kill confirm. An example would be Pikachu's f-air into up- smash. At around 90-100% this becomes a kill confirm, taking a stock. There is another type of kill set up called a kill mix up. This is dependent on your opponent's directional influence. If you guess their DI correctly you are guaranteed the stock, if not then you miss and your opponent will be able to get out.

 

Directional Influence

Directional Influence or "DI" for short is a technqiue that helps you control your momentum and where you are going to be launched. By using this technique you can survive much longer than usual. For example if Mario's forward smash were to kill you at 100% facing to the right, by holding the analog stick left you will survive due to you influencing the direction you go in. When DIing you want your analog stick to face the opposite direction if they are launching you horizontally and if they are launching you vertically you must press left or right.You can also use DI to escape a kill mix up. For example if Pikachu were to use his up-throw thunder kill set up, by DIing either to the left or right you can escape, if the Pikachu reads where you go, you will lose your stock. There is also "Smash DI" which is the mashing a specific direction on the stick to get out of combos.

 

Gimping

Gimping is when you use a move off stage and take away your oponnent's ability to recover back on stage by either sending them too far or too low. An example of this would be using Mario's cape and sending the opponent the opposite direction so they can't recover.

 

Reverse Aerial Rush

Reverse Aerial Rush or RAR for short is simply turning around in order to use your back-air instead of your forward air.

 

Parrying

Parrying is a mechanic new to Smash Ultimate, by releasing your shield at the perfect time you can parry an attack taking no damage and leaving your opponent open for a counter attack.

 

Teching

Teching is when you time a get-up so that you are able to immiediately act afterwards. You can also tech when you are about to be stage spiked (getting hit into the walls of the stage and bouncing back to the kill zone) to survive.

 

 

Combo Starters

Every character has combo starters, moves to that lead in to other moves. Combos change depending on percentages, but the great thing about smash is that you can make these combos as you go as long as you know where you opponent will be launched.

Frame Trapping

If you miss a move, don't be afraid! By using another move that is fast enough you can frame trap your opponent. Which basically is keeping your opponent inside the frames of your attack in order to restrict them from doing anything.

Staleness

This one is simple, by using a move too much it becomes weaker and weaker, once you use 9 different moves it will reset.