Even though I noted all three systems, I'll be doing from a Wii perspective since I own the Wii version. If someone else can give details noted in other versions that aren't in the description I give, please place them.
Taking place after Sonic Heroes (I do believe after Shadow the Hedgehog as well), the prelude to this story is as follows: Sonic, in hot pursuit of Dr. Eggman, begins destroying the villian's robots, one right after another. Then as Sonic was about to go head-to-head with Eggman's mech, he gets captured. In a swift moment, Sonic changed into Super Sonic (having collected the Chaos Emeralds before the fight) and free's himself. Eggman flees to a small space station, Super Sonic in tow, destroying Eggman's fleet along the way. When Super Sonic gets to Eggman finally, Eggman does the "Give me another chance, I'll reform" type of grovel. Sonic, having fallen for this since it was the first time Eggman ever showed remorse, starts to step away... right into a trap Eggman anticipated and triggered a device to seperate the Chaos Emeralds from Sonic. Using that same device, he switches the polarity of the Chaos Emeralds and fires a beam of pure energy to the planet, splitting the contintents apart, while the changed polarity of the Emeralds makes Sonic undergo a change in the absence of sunlight into a werehog.
Not giving any concern to Sonic in his new form, Eggman fires Sonic out of the spacestation back to the planet. When Sonic comes to, he sees a little creature who has a case of amnesia. Sonic in his current form, becomes worried that his re-entry may've been the cause of this character's amnesia, and so attempts to help him regain his memories.
Now for the gameplay: Things happen during the Day and During the night in each of the areas, mostly happening with Sonic and his two forms. During the Day, he moves about at usual true-blue speed, going from 2-D (sidescroller) to 3-D (behind-the back) views on occasion. At night-time, Sonic changes into his were form, able to extend his arms a good distance (enabling his attacks to reach a decent distance away and also enabling him to grab onto ledges he would not normally reach) and now also able to become stronger through the gaining of Dark Gaia Force.
In the Wii version, the control can be set up to use the Classic Control attachment, the Wii Remote with Nunchuk, or even the GameCube Controller, so if you're not familiar with the Wii setup, you can use other control variations that feel more comfortable to you.