The long running joke of the Street Fighter IV series, Dan is once again the weakest character in the roster.
Besides having a decent cross-up (jumping MK) and a pretty good Ultra, his special moves and combos leave a lot to be desired.
You'll need to Focus Attack to build up your Ultra as soon, and as safely, as possible. They really are key to winning the match with Dan.
Gadoken (quarter-circle towards + P)
Dan's fireball has no range, disappating around sweep range. It's not useful for controlling the screen like Guile's Sonic Boom or even Ryu and Ken's fireball but rather, acts as a combo ender.
Shoryuken (towards, down, down/towards + P)
His only decent wake-up move. EX adds more needed extra range to it, so it becomes a useful tool for hitting distant jump-in attempts with.
Dankukyaku (quarter-circle back + K)
By far Dan's best move. The EX version is a decent combo ender while the MK and HK versions should be avoided. You want to use the LK version, both on the ground and in the air, because ranged properly it's safe on block. It also breaks Focus Attacks, which is a great extra property for a move you'll be using so often anyway.
Hissho Buraiken (quarter-circle towards, quarter-circle towards + P)
A slightly disappointing super, as the range on it is deceptively poor and it leaves Dan wide open if missed. Save it for guaranteed situations or use the meter on frequent FADC combos and moves instead.
Legendary Taunt (quarter-circle towards, quarter-circle towards + HP + HK)
Dan's famous super. He rolls towards his opponent slowly taunting, doing no damage and is unable to block during it. It would be a completely useless super, except for...
Shisso Buraiken (quarter-circle towards, quarter-circle towards + PPP)
...the fact that you can cancel into the Ultra at any point. This means you can trick your opponent into sticking out a limb and go for the Ultra. Otherwise, use the Ultra as a move to hit jump-in attempts, Focus Attacks, blocked moves and so on.