Movement
Because the game is true in 3D, and you're able to step in and out of the screen with sidesteps, the movement is very interesting. Add in the fact that you can back step and dash, and that both of those can be cancelled, there's a lot of stuff to focus on for movement so you don't get overwhelmed. Don't worry if you can't get the advanced stuff, just come back to it once you feel more comfortable.
This section will focus on taking a closer look at all the specific weird movement types and how to best use and apply them.
Tools
SIDE STEPS (SS)
Input as a quick tap up or down (u/d), Don't hold the direction, as you will just crouch or jump. It's a great tool for avoiding straight-on attacks or moves with poor tracking. Can be cancelled with any attack or stick movement (only in TEKKEN 7). Some moves can only be done while sidestepping.
BACK DASHING (BD)
Back dashing is input with two quick back presses (b, b). Amazing for getting space on your opponent and covering it quick. Relatively safe, as you are still in block while retreating. Can cancel this into a crouch. (See KBDC below.) Incredibly important to apply when you don't feel a low coming. Most of the movement is in the later part of the animation.
FORWARD DASH (ff)
Input with two quick forward inputs (f, f). A lot of moves require a dash in order to use them. Can be cancelled with a crouch. It is easier to move forward than back generally in TEKKEN. This is no different, but be wary of moves and transition back to block if you need to quickly, but you'll still be open to attacks on the beginning of the dash.
RUNNING (f, f, n, f)
Running is just three forward inputs, but when input on a rhythm with two quicks then a small pause, you can quickly go from stationary to WR (while running). Cancelled by crouching or tapping back. A lot of moves can only be done while running per character. Typically good for fast sloppy pressure.
A WORD ON JUMPING
Unless you are Akuma, Eliza, or you have a VERY SPECIFIC PLAN, pretty much never jump. Jumping as part of a move? Cool. Your character has some wild shit they can do after jumping? Possibly cool, but sounds dangerous. Just jumping? NOPE. No way. You can get caught by basically everything, and even a jab can lead to a huge combo against you.
Advanced Techniques
Both are broken down by a top player here!
KOREAN BACK DASH CANCEL (KBDC)
There's plenty of videos for reference, but basically, it's the act of quickly cancelling backdashes with crouches. There's easy and hard methods and frankly, the videos do a better job explaining than I do.
[UNDERCONSTRUCTION]
"WAVEDASHING"
Sort of like KBDC but forward. Some characters like Mishimas (Kazuya, Jin, et. al.) have a way of cancelling crouch dashes with crouches in order to move extraordinarily quickly towards the opponent.
[UNDERCONSTRUCTION]
Application at Large
Here are a few thoughts on movement and why and when to use the tools:
Backdashing and side stepping are complementary. Backdashing serves to make space, side stepping is used to dodge staright attacks. Moves with good range often have bad tracking, and moves with good tracking ususally have questionable range or long startups. So in an ideal world, you would outspace a tracking move with backdashes, and you would sidestep a ranged, straight move with side steps.
Both serve the purpose of damage mitigation, and are invaluable for a solid punish game. Consistent and quick space control is important! You should be very comfortable cancelling between the two in order to paint a better strategy.
Once you have that down, you should always be moving. Transitioning from offense to defense is quick in this game, and taking the initiative in TEKKEN requires patience and positioning. Give yourself the advantage before you exchange hits. Make a good situation for yourself based on your position first, then go in and make something happen.