Following the pattern of my other guides, I'm going to be going over a specific move and all its many uses:
S Raeisageki (63214S on the ground) is, in many situations, a very risky move. It can be airthrown on reaction by some, and has a lengthy startup that makes it rather easy to beat out. Still, it has some very cool applications and should not be overlooked.
So first off, The Basics:
Raei's most obvious application is as an overhead crossup. While it is slightly faster than most IAD crossup options Axl has (Not Kokuugeki!), it's still rather slow, so your goal here is to catch the opponent by surprise. The main variables to keep in mind are spacing and momentum. The move can cover up to about 80% of the screen at a full run, but at a standstill, it covers about match-start distance (IE it will cross an opponent up at match start.) It's good to get a feel for about how far you'll go, and at what distance you can hit the opponent without crossing them up. Obviously, this can be done standalone, in oki (safest), or in blockstrings, or even when hitting the opponent (I would say this is the most likely to catch them off guard, although typically it's better to just finish your combo).
Meterless combos:
There are three basic things you can do with a Raei with no meter. Either Rensen for a bit of extra damage (Honestly, I usually skip that to save more time to set up my oki), a running Rashousen, timed to hit meaty (Running rashousen input is [4]6[6]H,) or, if you're in the corner, a standard B-Loop off a launcher. 3P and c.S work fairly well.
Anyway, this easy stuff is boring, but I figured I'd put it down just to be complete.
NOTE: Stuff most people already probably know ends here.
Advanced meterless tricks:
The "Safe" Raei: If you get some running momentum behind it, you can get a very far-reaching Raeisageki crossup without really putting yourself in danger on block. The crossup will happen, and on block, your momentum will carry you way the hell out of the way of any attacks that could come at you in the 6 frames disadvantage you're at (All hail level 5 moves!). Down side is that you can't really follow up if you hit without spending some meter.
Landing on the wrong side: Under certain circumstances, a counterhit non-crossup Raei with running momentum will allow Axl to land on the other side of the opponent before they can slide under him, thus making them slide towards him. Don't expect this to happen in many matches, but if it does, just start with whatever you start corner combos with and then do a standard air combo.
Running versus not running: In the corner, Raeisageki (hit) can be very punishable. The opponent can hurt you pretty bad if they're able to block it, so what you have to do is cut your run (Either by FDing or some other means) before going for a non-FRC'd Raei. This actually opens up a pretty good mindgame for people who don't have the knowledge or timing to punish it (Has to be a well-timed IB into walk forward --> throw if you do it right.) I will often do Raei (blocked) 2K, as it will usually get me under whatever quick jab the opponent thinks will punish you, and bam. Free corner combo. In addition, if you're just barely going to cross up with a run, you can often cut your run and hit a non-crossup point that actually looks like it will cross up, and vice versa. Learning to kill your run fast and Raei is an invaluable tool you can use with no meter (and probably will have more opportunities to than you will to do the tricks listed below.)
FRC tricks (No JI):
Raei FRC was improved in AC, and now has a three-frame window. However, since only the third frame hits, it's best to think of them as two separate FRCs: A hitting one, and an empty one. This also means learning the 1-frame timing for the hitting FRC. If this is too hard for you, don't read the JI section.
The easiest game to play with Raei FRC is a potent High-Low-Throw-Crossup game. This works best on Oki, but can also of course be done naked or in blockstrings (Some opponents can react and airthrow, however). Non-hitting Raei FRC can be followed by a throw, another high (j.K, j.H, j.D, and Bomber are good, and you can even do things like j.H-->Bomber/2K to be extra tricky), a Kokuugeki (Basically to punish jumps) or a low move (2K is best.) This is all in addition to the judgement as to whether the move will cross up, and can make for a very tricky and intimidating mixup situation. The hitting FRC is really better if JI'd, but you can still go for additional overheads or land-->low. Of course, if the opponent blocks well, you've still got your pressure going, as most of these options either give frame advantage or can gatling.
JI Raeisageki:
With a Jump installed, you have even more options. A jump-installed Raeisageki allows you an additional jump after the FRC, which can play games with an opponent's AA, but more importantly, you have an airdash, which gives you a way to combo off Raeisageki midscreen. A fairly standard combo would be:
632147S (the 7 JIs it) --> Airdash toward, j.H, 5K, 2S, j.D, Kokuugeki.
The j.H must be done while falling. It will hit any character, but against low sliders, it has to be done even later. Naturally, this can work like any other air combo, which means FB bomber to get to the corner can replace the Kokuu, and if done into the corner, Kokuu can be replaced by bomber loops. Notably, the j.H-->5K can be substituted with j.S and 5P respectively as needed to connect from further away. (Good for running setups that overshoot the opponent a little)
So now you have a much more damaging and dangerous move for just 25% meter. This is not only a useful tool for damage, but also makes getting hit by Raei a much less attractive prospect for your opponent, which will make them think more about blocking it the right way (adding the threat of damage to the mixup situation) Additionally, there are several more mixup and safety options open to you:
For one, you can go for double-crossups, such as JI Raei-->Empty FRC, airdash back, j.H (double crossup.) Kokuugeki is an especially potent crossup, as it comes out quickly, stops your dash momentum (and thus can be very ambiguous,) and can be FRC'd into big damage. Being a projectile also makes it difficult to beat. This also allows you to run away with a jump or an airdash if you think the situation is not in your favor.
Of course, while you're dancing around in the air, you can just get airthrown. This is why it's often useful to have the Raei get blocked and FRC on the third frame. From here you can go for a re-crossup game, as well as all aforementioned mixup, but you can also very easily continue your pressure with an airdash back into j.S, which keeps the opponent blocking while you land.
Additionally, a JI'd Raei can be used to chase an opponent that tries to backdash away from a raeisageki to avoid being crossed up.
Special notes:
Low Profile: The hitting FRC won't connect against "low-profile" stance moves, but the move itself will. The FRCable first active frame of the move will reach crouching opponents (not Faust, though) but doesn't quite reach the ground yet) Probably RCing it in order to get a combo isn't usually going to be worth it, but it's something worth knowing.
Turn-around: To get Axl to turn around immediately after the FRC, you have to SJI the move, so if your intent is to combo from a crossup, you'll have to keep that in mind.
Anyway, hope this has been helpful, and I hope to see some of this used in more matches!
Do it really really fast.