Step 2: Baby Steps

NOTE: To describe input in this game, I'll be using the standard Japanese notation of input, where each direction is represented by a number:

7 8 9
4 5 6
1 2 3

These directions are given assuming the player is facing right. So, pressing 6 would move forward, 4 would move backward, 236 is a fireball motion, 623 is a dragon-punch motion, and so on.
If a direction is in bold, that means you hold the stick in that direction.

On top of this, Blazblue has 4 buttons:
A = Light
B = Medium
C = Strong
D = Drive

A, B, and C are pretty easy to figure out, but Drive moves are wildly different depending on the character. For example, Ragna gets his life draining moves, Jin gets his freezing moves, Bang gets his counters, and so on. We'll leave going into detail on characters' specific drives for later.

[There is also a Taunt button, but besides one extremely character-specific use it serves no real purpose. We'll ignore that until it arises.]

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Movement

One of the biggest differences between Street Fighter and Blazblue is the way they handle movement. While in Street Fighter your movement abilities are basically limited to 'walk, dash, jump', there's a large variety of potential movement options in Blazblue. Here's a rundown on what's available to you.

Walking

Walking is more or less as it is in Street Fighter. Hold 6 [forward] to walk forwards, and 4 [backwards] to walk backwards. Hardly ground breaking stuff. Note also that walk speeds are typically much slower than in Street Fighter. That's because Blazblue focuses much more on...

Running

Pressing 66 - that is, tapping forward twice and then holding forward - will cause your character to run across the screen. This is a much different system from Street Fighter, in that unlike SF you aren't forced to dash a certain distance. You can run for as long or short as you want, although it does have a small amount of startup. You can also cancel into attacks from running, and indeed this is vital for many Blazblue combos.
[NOTE: A few characters are unable to run, instead having dashes that work in the same manner Street Fighter's do. The only exception to this is Tager, who being the main grapple character cannot either run or dash.]

Backdashing

44 is your backdash - a quick way to step out of the field of battle. Better still, most characters are invincible for a good length of their backdashes [Hakumen being the only exception], but they aren't totally unpunishable and force you back into a neutral position.

Normal Jumps

Pressing 7, 8 or 9 will allow your character to jump into the air. 7 produces a backward jump, 8 a neutral jump, and 9 a forward jump. Again, this works more or less like Street Fighter does.

High Jump

If you're familiar with Street Fighter IV, you'll know that C. Viper has a High Jump move. Basically, by pressing down and then quickly jumping up, she can perform a higher jump than usual. In Blazblue, this system is also present, but this time every character can use it.
To perform a high jump, press a down direction [1, 2 or 3] and then jump in whatever direction you want. If you've done it right, you should jump considerably higher than normal.
[Before you ask, no, there are no high jump cancel shenanigans. This game is complicated enough already, goddammit.]

Double Jump

If you're one of those greedy assholes who isn't happy with one jump, Blazblue's nice enough to give you two. When you're in the air after a jump, you can press 7, 8 or 9 again to perform another jump in mid-air. This allows you to gain height, continue combos, and generally add mixup to your game and give your opponent a headache.
[Note: Taokaka can TRIPLE jump. Tager cannot double jump.]

Air Dashing

And just in case you aren't satisfied with your air movement options, you've got an air dash as well. Pressing 66 or 44 in the air will allow you to dash forwards or backwards respectively. However, note that you can't air dash and double jump in one jump, so you have to choose carefully.
You can also perform attacks in the middle of an airdash while still carrying your forward momentum, which is great for pressure.

(The fastest way to perform a forward airdash is 966 - up-forward, forward, forward. Alternatively you can use 956 - up-forward, let the stick return to neutral, then forward.)

[Note: Once again, Tager can't airdash. Sometimes you've just got to feel sorry for the guy...then you remember he's high tier and stop feeling bad.]

So in short, that's the movement options Blazblue offers. Up next is the part everyone's interested in - attacking! >:3