The members of the SRK community really know their stuff when it comes to playing Street Fighter competitively. As a matter of fact, I gained most of my SF related knowledge by lurking and reading on SRK's forums.
But I think that what I like to call "new-school" type of fighting games are often misunderstood among the SF players. By that I mean games like the Guilty Gear series, Melty Blood series, Arcana Heart, Blazblue etc. etc.
Many SRK members look at a SF game and see the flow of the match, the gameplan, the spacing, the mind games etc. etc., but when they look at NSFGs (New School Fighting Games) all they can put their fingers on are the combos, which means they can only see the most basic and obvious part of the match.
I think after a player gains deeper understanding of how NSFGs work, he will be able to transfer his SF fundamentals into this type of games as well.
So this guide will help you to understand NSFG using your existing knowledge of Street Fighter. (Feel free to correct me if you see something that bothers you. I should note that I have read the MBAA guide for SF players on Melty Bread but I wanted to do something more general and less game specific, since MBAA is a unique beast of his own.)
Since I love the format Maj used for his SF handbook, I'll do something similar, giving plenty of video examples.
Part 1- Movement
This is the 1st brick wall we encounter when switching from SF to New School.
The golden rule of SF is that being in the air is worse than being on the ground, since in the air you can't block, you can't do more than one attack and you can't really move. (You are moving but you are stuck at the predetermined course you committed on 2 seconds ago when you pressed either u/b, u or u/f)
Those big limitations make jumping a risky option. In NS though, it's different- You have options now! You can block most of the stuff coming at you, and you can move around the air by doing double jumps and air dashes.
That said, air movement does have some limitations:
Air dashes are somewhat risky (We will refer to that later), and you are still "stuck" in your new predetermined course after using all your aerial abilities until you hit the ground.(While your grounded opponent can position himself at the angles he can deal with you at ease, or even jump and interact with you from the air) You also can't block some ground moves while being airborne (Like in SF Alpha games) unless you use some form of advanced defense that requires strict timing and/or is limited by a gauge. (Be it the super bar or it's own bar)
So while limitations still exist, air movement gives you enough freedom and versatility to make up for it, so you will be jumping around a lot.
1.1-Jumping and Double jumping-
This is an alternative way to move around. Depending on the matchup you might want to get to your opponent from the ground, from the air, or both equally. It's really all about the angles and ranges and where you have the advantage over the opponent's character.
Your character's normals are critical at controlling space while you are traveling the air.
It's pretty common to see players jump and on the way up use a normal with a fast startup and a fast recovery (usually a light attack) and then do whatever they wanted to do, be it to air dash backwards or land on the opponent with their preferred normal for jump-ins.
http://www.youtube.com/watch?v=fM2z93PVM-8#t=2m14s
The weak normal at the start of the jump is a safe
http://www.youtube.com/watch?v=uMy2auKtTYQ#t=3m06s
"option select" in case the opponent did decide to come to them from the air at the same time, so it's actually a very solid anti-air. You can also see the characters using aerial normals that have long horizontal hitbox, right before they land from a jump. This is another safe way to control space.
http://www.youtube.com/watch?v=MUf7fTmMQR4#t=1m19s
Landing on the ground prevents the normal from having any recovery, and it can hit opponents who try to run at you from the ground as you land.
http://www.youtube.com/watch?v=INe5xXjMrT8#t=2m11s
Double jumping is used to mix up the options you have to approach your opponent, after you already committed to a jump.
Let's say both you and your opponent are jumping at each other. You can try to beat his air to air move with your air to air move, or you can quickly double jump, and while he's doing his air to air move you attack from above him with your to ground move. You win.
Another good example is when you are jumping at a character that has great anti air move, but with slow recovery. Use a neutral double jump at the last moment to make him whiff the move, then land on him as he recovers, with no time to do another anti air or even to block.
You can also use moves that keep you in the air for the same purpose.
http://www.youtube.com/watch?v=c_UmlLNjK7g#t=1m15s
Just remember that if the opponent predicted that and did nothing, you are out of movement options and are stuck landing at him, giving him the advantage.
1.2-Air dashing-
Forward air dash- IMO this is the New School equivalent to jumping forward in old school games.
It's that risky option to get in someone's face and not being able to block while doing it, just like jumping forward in SF.
http://www.youtube.com/watch?v=D4qJ4rMEh8A#t=3m56s
You can even consider it being a riskier option because in SF you can use your 1 aerial move at different times to counter different anti airs. For example use it late to deal with a Dictator's s.HK or use it early to prevent him from jumping at you with j.MP.
But you can't do anything during the beginning of your airdash. No blocking, no attacking, nothing. You are a sitting duck. Umm, more like an airdashing duck actually.
As such, you won't see it being used much in matches, excluding specific cases where it's much safer, such as chasing an air back dashing opponent,
http://www.youtube.com/watch?v=MUf7fTmMQR4#t=1m25s
or to dash high above the opponent to the other side of the screen in order to avoid the corner.
http://www.youtube.com/watch?v=7SOv52LpzvY#t=56s
Backwards air dash- This is used to quickly gain some space between you and your opponent.
http://www.youtube.com/watch?v=D4qJ4rMEh8A#t=6m18s
It's advised not to start it when you are really close to the opponent, since you can't block while doing it.
http://www.youtube.com/watch?v=uMy2auKtTYQ#t=4m24s
At range zero you have other tools such as jumping back while blocking and the ground back dash (which works exactly like back dashes in SF4, which some invincible frames on the start, and vulnerable frames at the end)
http://www.youtube.com/watch?v=xx5_UczdEMI#t=21s
As with jumping, after the aerial backdash you use your big horizontal move to catch pursuers.
http://www.youtube.com/watch?v=uMy2auKtTYQ#t=1m36s
1.3- Jump-in mixups, using all your available options-
Once you have them in a situation they won't anti-air you (either they can't or they are scared to push buttons because of your high priority jump-in option), it's time for a jump-in mixup.
The first option is to air dash at the last possible moment and attack from there.
Unlike a regular jump-in, the timing they need to block this is exactly as if you just landed and attacked low. So it's a true mixup.
http://www.youtube.com/watch?v=3Uod1Eg5e54#t=3m30s
The second option, like I had just told you, is to empty jump into a low
http://www.youtube.com/watch?v=27ZvzmL1Wiw#t=4m34s
You can even whiff the aerial normal to hide your real plan better…
http://www.youtube.com/watch?v=xc9Mmz2VESQ#t=1m16s
The third option is to empty jump into throw
http://www.youtube.com/watch?v=MUf7fTmMQR4#t=34s
Instead of an air dash, you can also use an overhead special that leaves you airborne while normally you should have landed already.
http://www.youtube.com/watch?v=nrxFRbHrgxs#t=1m58s
Or use a jump-in that is 2 hits instead of just one, and expecting you to land and do a low, the opponent will won't block the second overhead hit.
http://www.youtube.com/watch?v=xc9Mmz2VESQ#t=1m04s
How about faking a crossup using an air dash?
http://www.youtube.com/watch?v=xc9Mmz2VESQ#t=03s
Or using an air dash to mix up which direction your opponent needs to block you projectile?
http://www.youtube.com/watch?v=PUgXwUSz05k#t=3m16s
Make sure to check out all the tools and options your character has to make every opportunity count.
1.4- Ground movement-
When both players choose to stay on the ground, the game will look similar to SF, but only with running and some sort of a way of faking it. Arcsystem games let you cancel the running momentum with the advanced blocking mechanic so it's used a lot as a spacing tool.
http://www.youtube.com/watch?v=uMy2auKtTYQ#t=2m58s