Smash is the Red button on the main menu of the game, and is the mode where standard matches take place. They can occur as Solo matches (against CPUs or amiibo) or as Local Multiplayer Battles, in which the host can put up filters to only allow friends into their server.
After selecting either Solo or Local Play, players select one character from the selection screen, and select a CPU (if they so desire) and its level. By clicking the word "Time" or "Stock" on the touch screen, players can change the rules of the battle, such as making the match either Time or Stock, adding or removing Items, Handicapping, etc. Rule changes can only be made by the host of the battle, i.e. Player 1.
By far the most common type of match is Stock. In Stock matches, players have a set number of lives (default 3), and will try to reduce their opponents' lives to zero to win. By changing rule, a time limit can be added to a stock match, and players will go to sudden death if a winner is undecided and two or more players have the same amount of lives by the end of the time limit.
Time matches are free for all battles occurring within a set time limit (default 2 minutes) and will compete to knock out opponents as many times as possible. The game keeps track of this by keeping "scores"; players gain +1 for every kill they make and -1 for every death they take as well as suicides (although this can be changed in the rules). The player with the highest score by the end of the time limit is declared a winner. If a tie occurs, players will enter sudden death.
Sudden Death occurs when a winner cannot be determined normally. In sudden death, contenders with the same scores in time matches or stock in stock matches are sent into a one stock fight. The twist is all players in sudden death start the match at 300%. Also, if the match lasts too long, explosives rain from the sky in attempt to end the match quickly. The survivor wins the match.