BBTag/Movement

Ground Movement

Dash: To run forward, press or hold Template:6 on the ground. Some characters do not have dashes like Tager and Waldstein. Other characters have unique forward dashes like Azrael or Hazama.
Backstep (Backdash): To perform a backstep, press Template:4 Template:4 quickly. Backsteps have a bit of invincibility on start-up, making them useful tools to avoid attacks.
Ground Ukemi (Ground Tech)

When your character is knocked to the ground, your character will automatically flash white and flip off the ground. This entire animation is invincible, but it is slow, thus giving your opponent time to set up a mixup. You can hold forward or backward to tech in either of those directions.

Air Movement

Air Option: Aerial movement in Blazblue Cross Tag Battle (and most Arc System Works titles) work on a either/or system - you can either double jump or air dash, but not both. Doing either is called using an air option, and most characters only have one air option. Air options are regained once the character touches the ground, performs an aerial ukemi, or after air blocking.
Jump / Double Jump: Press any of the upward directions to jump. Ground jumps have X frames of start-up where you are still considered on the ground and are invincible to throws and command throws.
High Jump (Super Jump): To High Jump, start from Template:5, then quickly press any downward direction, then any upward direction. High Jumps have start-up just like normal jumps. They are used to create vertical distance between you and your opponent as well as to run away; High Jump over the opponent, then air dash away!
Air Dash Forward / Backward: While airborne, press Template:66 to perform an air dash forward, and Template:44 to perform an air dash backward. Air dashes are used to cover large distances quickly, but they are vulnerable during startup.; A common tactic is to perform an air dash immediately after jumping in order to cover distance quickly and avoid ground attacks; in fact, this tactic is so common that it has its own name: Instant Air Dash (IAD). IADs are performed by pressing Template:9 Template:5 Template:6 for a forward air dash and Template:7 Template:5 Template:4 for a backward air dash. The idea is that the jump includes a directional input that also counts as an input for the air dash command.
Aerial Ukemi (Air Tech)

Hold a button and pick a direction with Template:4, Template:6, or Template:5

After getting hit in the air, hold the button down while you are getting hit in the air and you will Aerial Ukemi as soon as possible. By holding left, right, or no direction at all, you can choose the direction you recover.

Aerial Ukemi takes X frames and you are fully invincible the entire time.

Usually, you will want to ukemi immediately when possible, but opponents can take advantage of this behavior by setting up a mix-up that you will be forced to block when you ukemi. A common counter to this tactic is to delay your ukemi in order to throw off the opponent's mixup timing, but this carries some risk.

Cancels

Arc System Works games typically have a lot of types of cancels, but they mostly serve the same purpose: to let you freely create combos and blockstrings. Don't be too overwhelmed, these will come second nature to you after playing enough.

Revolver Action: Each character has the ability to cancel certain normals into certain other normals specific to that character. Please consult your character's wiki page to find out more.
Smart Combo: Each character has a combo that can be done by rapidly pressing the or button. More information can be found here.
Special Cancel: Most normal attacks can be canceled into Skills. This is generally used to extend or finish combos, but can have other applications as well.
Super Cancel: Instead of canceling a normal attack into a Skill, you can cancel it into a Distortion Skill or Astral Heat instead. Since Distortion Skills typically have long recovery and/or knock the opponent away, this is usually used as combo ender. Note that unlike most ArcSys games, you cannot cancel a special move into a Distortion Skill or Astral Heat unless your active character is in Resonance Blaze.
Jump Cancel: Some normal attacks can be canceled into a jump or high jump. This is used in combos as well as block strings and mix-up. Many attacks can only be jump canceled on hit.
Active Change: By pressing during a Partner Skill, you can cancel your partner's current animation into an immediate character change. The cancel itself has an animation with recovery, so proceed with caution.
Cross Combo: By pressing + during a Partner Skill, you can cancel your partner's current animation and keep them on screen, allowing you to continue using Partner Skills by pressing attack buttons at the cost of all of your Cross Gauge once you reach 50% or more.
Distortion Skill Duo: By pressing during your character's Distortion Skill, you can cancel your character's Distortion Skill into your partner's Distortion Skill for 2 additional Skill Gauges.