Assist characters don't physically appear, but rather create props similar to crewmates in Nick Kart after flashing a JPG with a non-voiced quote in a speech bubble on screen (so, for example a Chicken Little assist would have the speech bubble "The sky is falling!").
Most assist characters are defensive and there are 3 assists for each possible ability, ranked by stars - each uses up one slot for every star, you have 4 slots. The more stars, the more charge a character needs - charge in 1v1 or team battles is based on damage delt, while charge in free-for-alls is based on damage recieved. You use your assists with the D-pad, similarly to how you access taunts in Smash. While fighters are near-exclusively drawn from the animated canon and Pixar, assists can be anything Disney (except Marvel, Star Wars, or Fox - though Blue Sky characters could maybe show up, and Big Hero 6 is obviously on the table) Some examples of abilities would be...
DAMAGER CLASS - Hits 10 times without causing flinching or knockback, can be mashed away
Baby Sinclair - A frying pan appears on a foe's head that deals 1.20% damage each hit, for a total of 12%
Club Penguin - throws snowballs from beyond the 4th wall that deal 2.50% damage each hit, for a total of 25 damage.
Dr. Facilier - Makes a voodoo curse that deals 3.50% damage each hit, for a total of 35% damage
BUILDER CLASS - Builds a soft platform only their summoner can use
Chicken Little - a sky piece falls and stays out for 5 seconds
Phineas and Ferb - two wooden platforms are built and stay out for 10 seconds
Fix It Felix Jr. - four golden brick platforms are built and stay out for 15 seconds
SNOOZY CLASS - puts a foe to sleep for 6 seconds
Mrs. Jumbo - Sleeping foe cannot be interacted with at all
Evil Queen - Sleeping foe can be hit or grabbed, but will wake up
Andy - Sleeping foe can be damaged without waking up