When I understand you correctly, you want to know how you can move your character around and so that it also uses the animations.
When you begin something like this, try to first separate the visual appearance from the functionality. A good start is to setup a basic scene, with a floor to walk on, a box collider2D (I assume).
Make an empty game object. This is usually called the "Holder", and place it on the ground. The holder will contain the logic, and the character graphics will be dangling inside as a child object. Later.
It's recommended that 1 unit should be roughly 1 meter, or 1 tile. Toogle the grid on (button above the scene view, or [G]. Next, I recommend to make a folder for primitive sprites. Right click into it and create a square.
Drag the square into the scene, and into the Holder. Give it the proportions you want, for example 2 units high and 1 unit wide, and in the sprite renderer you can also set the colour. This thing will represent your character for quite a while. Also pick a nice background colour in the camera for good measure. I typically give it a "beak" with the triangle so that I know in which direction it's facing.
Add a box collider 2D, or a capsule2D and a rigidbody2D to the
Holder. Freeze the rotation Z. When you hit play, the "character" (i.e. the rectangle) should be standing on the ground.
Next, you want it to move. Add an FSM, name it properly. In a typical first beginner setup you need these actions:
-- GetAxis with "Horizontal" (the exact name is listed in the Input Manager). Store the input. Multiply it with the desired move speed.
-- Set Velocity, and make sure to only set the x value from the input axis result.
(all of these are every frame!)
You should be able to move the object around, using physics. At least with the placeholder it should work. There are about 1001 other and better ways, but that should be a decent start to get it going.
I
strongly encourage you to ignore the animated character for quite a while and get the movement logic and such to work nicely, and get something functional using just the primitive placeholder.
The tool in Unity for animation is called Mechanim. It's notoriously clunky to use.
But since you asked. Here's how you would generally proceed. For the Animation you then add also:
-- Set Float (every frame), and store a duplicate into a new Float Variable, which we'll use for the Animator.
-- Float Abs (every frame): this makes new float only go in a positive direction. I.e. when you idle, it's 0 otherwise it's some positive value.
-- Set Animator Float (every frame): this sends the new (Float Abs result) variable over to the Animator. It totally depends on how your asset does it. Probably it has an Animator on the "character" they provided? If so, you want to drag your character in where the placeholder is, and switch off the placeholder for now (but keep it for later prototyping). Then set this character object into the action, so it recognises that animator.
-- Head over to the Animator and make a parameter, e.g. "horizontal". Or check which ones are already provided. And use the same name as parameter in the Set Animator Float action.
I generally avoid mechanim and use PlayMaker instead. To do this, I make use of a lot of blend trees that cut most of the clutter. For example, idle and movement can be done using one blendtree. The entire jump arc is one blend tree etc. I then use Animator Cross Fade action (from Ecosystem) to set specific animations I want. You have to see if you can butcher their setup, or maybe it's nicely organised.
In the traditional way, you have to make parameters in Mechanim (or find out which are there). Use the various Animator actions in PlayMaker to trigger, set bools etc to go to the correct animation state. Open the Actions browser and head to the Animator section to see what's available..
If that works. Tackle the flip. Add a float compare, and a set scale. Duplicate the entire state . Call one state "Facing Right" and one "Facing Left", each with an event "flip to left" and "flip to right" etc. The right one checks every frame if input is below -0.1, then go to other state. And the Facing Left if the input is above +0.1. In the Facing Left set the x scale to -1, and in the right one to 1. This should work as a first setup.
Once more, this should only get you going. Later you want to separate the logic into different FSMs, and there are better ways, but that then depends on what exactly you want to achieve