First and most importantly, only certain stages are available for 8-way fights. Screenshots show a Super Mario Galaxy stage, the Xenoblade stage seen in Super Smash Bros. for Nintendo 3DS, the Earthbound stage, and the Twilight Princess desert scene. The site does not specify if these are the only stages available for 8-player fights.
Those fights are restricted to Stock (set number of times you can be knocked out) and Time (knock out as many players before the clock runs out) settings. Players can split into as many as four color-coded teams of two as well.
How will these fights control? Players can use as many as eight Nintendo 3DSes or eight Gamecube controllers, but there are some restrictions. Only seven Wii remotes or Wii U Pro controllers can be used simultaneously, and Super Smash Bros. for Wii U only supports a single tablet GamePad. Plan those Smash parties accordingly.