how is it for single player?
Hmm, well, I'm not an expert, but from what I've played so far... you have your Classic, All-Star and Stadium modes with the latter including Multi-man Melee, Home-Run Contest and a variant of Target Test* which has you beating up a bomb which you then launch at the targets to see how many you get (so a bit of a hybrid of HRC and TT).
Classic uses an intensity slider like that used in Kid Icarus: Uprising. The default is 2.0 and you can increase it up to 9.0 - but if you lose a match on a higher intensity, it will automatically be lowered, so you'll have to go through without fails if you want to clear a certain intensity.
All-Star mode can be played at any time but is only complete when you unlock all characters, which is actually fairly simple - if you just play a lot of normal matches against the computer, you'll face a new challenger every 10 battles, and they'll appear after every match until you unlock them.
As for the exclusive Smash Run mode... I've only played it once, but from what I've seen, it involves five minutes of exploring an area where you fight different Nintendo enemies and get stat increases when you defeat them. At the same time three other computer-controlled characters are going through as well (though you can't interact with them AFAIK). At the end you'll be put into a one minute match against the computer characters with all the stat boosts you collected and whoever wins that is the winner of the whole thing.
Probably not my favourite mode but I suppose some people might like it.
Also you can now customise any character - not just Mii fighters - depending on the equipment you've collected in any mode and that character's different choices for special moves (if I recall correctly - I haven't really done it myself yet).
Anyway, that's what I've experienced so far while playing as I've mostly stuck with normal matches so I haven't explored the other modes thoroughly, but I hope that's helpful!
*Melee title - Break the Targets/Target Smash in 64 and Brawl respectively.