Okay, so I'm not sure what the new difficulty settings are (I think I have them correct, but I'm not 100% sure), so I'm gonna call them :
Blue - Beginner, first level you learn. Didn't exist when I started playing ^_^
Yellow - Standard? I know it as "light".
Red - Difficult? I remember it as "trick".
Green - Heavy? It was "maniac" back in my day.
Purple - Challenge. I'm not even gonna bring it up
This might come out kinda gamefaqs-y, but it's the best way I know how to explain these concepts. There's only a few major ones you need to have down-pact.
When you first start playing, getting better is mostly learning to stop re-centering yourself.
Super-beginners will do this often. Keep in mind, DDR doesn't penalize you for standing or stepping on a note that isn't there. If you step on left as it comes up, don't lift your foot, leave it there. When right shows up, step on it. Now you have both feet on either side. If left comes up again, just lift that foot and step again. If up is next, just move your left or right foot up. A good idea is to press it with whichever foot you didn't just step down on. Essentially, you'll learn over time how to shift your feet so you can hit arrows as they come. This is the most important first step.
The most important second step (this is assuming that very little in the yellow gamut and nothing in the blue is giving you a problem) is to learn how to hit the "in between" steps (e.g. the notes that are differently colored and show up between two regular notes. Essentially, half a beat between each note instead of a beat). This is mostly practice to get down. Try songs that only have a smidgen of quick steps. Brilliant2U was the old mainstay I used to try to teach people this, it's also the song I used to learn the fast steps myself. Look for the easiest red song you can find. If it has only one or two of those segments every little while, play the song until you get it down. It's nothing but an extra beat, if you can do it once, nothing but practice is stopping you from doing it consistently. Eventually, you'll realize that most songs in the red level stick to that set of three notes in a row. Some just use more than others. In green, you'll get what's essentially a superspeed version of this set of notes that's a quarter of a beat between each one instead of half. Watch out for this one, they sneak it into a lot of green songs, and usually inside of a mess of other fast notes.
Finally, you need to know the gallop. AFAIK these notes are exclusive to the green difficulty, but some might show up in red. Basically, these are notes that are like "right next" to each other (quarter of a beat, possibly an eigth). Usually you'll get a lot of "pairs" in a row, that are seperated by a beat each. It takes some time to get used to how they look. Good examples in green are Matsuri Japan and Tsugaru, and So Deep if you hate your legs. I think AM-3P had some as well. It's called the gallop because, well, that's how you play them. The easiest method I know of is to jump, but land one foot slightly slower than the other (basically, drop with your weight on the first foot to land), in relation to how the note asks you to. Also, big tip: MOST of these songs will require you to alternate which foot lands first after each beat. Keep that in mind while you're practicing them.
At this point, you'll know enough basic DDR movements to *pretty much do everything in the game. Literally, if you can keep from centering your feet, hit half-beat notes in sets of 3 or 5, and gallop, the only thing standing between you and, say, Healing D Vision or Maxx Unlimited is practice. A ton of practice.
This is usually the hard part, and I think this is the best advice I can give you:
Don't shoot to pass a song, and then to AA it. As soon as you can pass a song, look to pass it consistently. Getting a B or better should do it. Once you're there, move on to a harder song. Repeat and make your way up. Eventually you might get to a point where it stops being about notes you miss and starts being about running out of stamina. This is especially true when you make it to level 8/9/10 songs. With that in mind:
See if you can get yourself a copy of "Can't Stop Falling in Love: Speed Mix". It's the closest thing to "jogging" DDR has. If that's too fast for you, try "The Twist". CSFiL is the best song for building stamina. If you're doing half-hour or hour-long "sets", mix a few CSFiL's in there. Once you have that song down, you can start moving on to stuff like Break Down 'n Healing Vision Angelic.
The nice thing about the "get my butt kicked by a song until I can pass it and then move on" approach is that you'll notice, over time, as you make your way up the difficulty chain, that getting a AA on an earlier song you could barely pass before is as simple as playing it a couple of times, because all of those tricky passages you choked on before look like they're going in slow motion compared to all the stuff you can barely pass now
I'm not sure if this guide is going to be terribly useful, but I'm just putting it out here in case it can. Keep in mind, I just wrote this now, so it might look a little messy. If anyone needs clarification or fixes, I won't hesitate to add them next time I'm here.
* exceptions are songs with a bunch of "odd" notes, and songs that bunch notes super-close (read: Bag, So Deep). The former is usually just practice, the latter is practice and/or setting the speed to 2x or 1.5x
