First, get the textures you want to use somewhere in your Assets folder.
Open the palette panel from Unity toolbar, Window, 2D, Tile Palette.
Create a new palette with the grid type you want.
Save it somewhere like Assets/Graphics/Tiles/*Palette.
Select the textures you want to add to your palette, and drag and drop them in the palette panel.
Save it somewhere like Assets/Graphics/Tiles/*Tiles
Your palette is ready!
In Unity, create a tilemap in a scene by right clicking, 2D Object, Tilemap, and create the type you want.
You're now able to fill your grid with tiles from your palette.
If you want multiple layers of tiles (like to differentiate the ground from some props), create any tilemap you need within the same grid.
You can now select which active tilemap you want to paint on in the palette.
If you need animated tiles, first in Project Settings check the Enable Preview Packages in Package Manager settings.
Now install 2D Tilemap Extras in the Package Manager.
Now in Unity, right click in the project folder panel, Create, 2D, Tiles, Animated Tiles.
Open it, and add all your frames within it.
Now you just need to add it to an existing palette, and use it.