Help with basics of Nintendo switch system

Yes, in order to properly play the game, you will need to hold the controller with both hands. That's because Mario's movements are tied to the left analog stick while his actions (such as jumping) are tied to one of the many right-hand buttons. This is in particular vital to the many jumping sequences, where you need to be moving in one direction while jumping.

There are also a number of moves that are extremely hard to pull off one-handed:

• Long jump: Requires crouching while running and immediately jumping.
• Cap jump: Requires moving towards Cappy while holding the throw button pressed.
• Side Somersault: Requires running in one direction, then jumping immediately after turning in the opposite direction.
• Triple jump: Requires jumping three times in a row (with the proper timing) while moving. You can double jump without moving, but the triple jump requires that Mario is already moving before his first landing and second jump.
• Wall jump: Requires jumping towards a wall, then jumping right as Mario bumps into the wall.
• Swimming: Requires pressing the jump button as you move forward.
• Dashing (2D mode): Requires keeping the throw button pressed as you move either left or right.

There are also a number of capture-specific moves that benefit from two-handed control.

Fortunately, not all Moons/Stars must be collected to finish the game; since many of the game's Moons/Stars are difficult to find (well hidden) or get (challenging to reach), the game does not expect players to collect them all. Unfortunately, it does expect players to be using both hands, so the vast majority of Moons/Stars will be very difficult to collect with only one hand.

Not all Switch games require the use of both hands, but many do, and Super Mario Odyssey is one of them.