I describe it as "30% Deathsmiles, 50% Galuda 2, and 20% Soukyuugurentai". Percentages may vary from player to player, but the mix of those three games in DSII is pretty apparent to anyone who has spent some time with it and knows how to score. Quick summary:
Basically you get your counter up to 1000 and your multiplier up to 10,000 (or as close as possible) by absorbing red and blue rings. Shot gives you red rings that build up your counter, while laser gives you blue rings that build up your multiplier (some characters have it reversed). There's a proximity effect in this similar to the one in Galuda 2 and MFBL. Press A+B to go into fever (like DS), and you can use shot or laser to leech skulls off enemies and you won't have any suicide bullets to deal with. For high scoring, though, you need to use your lock-shot on groups of multiple enemies, often in the background (a la Soukyuugurentai). When they die they release slow homing suicide bullets (a la Galuda 2's zesshikai mode). When you let off lock shot these suicide bullets are converted to skulls. Time a lock shot right as the counter goes back down to 0, when there are lot of suicide bullets on the screen, and you can instantly respawn it back up to 1000 and go right back into fever mode (similar to the recharge technique in Deathsmiles, but much easier). Rinse and repeat. You can do the 'recharge' over and over in some levels (dozens of times), unlike DS where you could only do it once or twice in a level. It gives the game a very fast pace, and smooth rhythm.
There are no bouncing skulls (that break into smaller skulls) to deal with as in DS. You just absorb everything you can. Skulls you miss just fall off the screen.
In regard to leeching skulls off enemies with your shot, some characters can do this more effectively than others. Lei is the best at this, and he plays much differently from the other characters due to this. You can go through some stages with Lei just doing this and score well.
Your multiplier and counter carry over from stage to stage, but they max at 10,000 and 1000, respectively (just like the original DS). If you die you only lose 10% of your multiplier, which is quite nice. Your multiplier does not reset to zero when you exit fever mode, as it does in DS. It stays the same.
There is more to it, and there are some more advanced scoring techniques you can use with each character, but that's the gist of it.
Here's an all-clear run with Casper, showing all of this stuff in action:
989mil ALL with Casper: