The game begins by allowing players to choose from either Story, Trial or Practice Mode. (An Options menu is available from the main menu, as well.) For the full single-player experience, the Story Mode contains the substance of the game. From there, the player will be able to select the level, Yoshi (there are 8 Yoshis in this game) and which fruit will be "lucky" (see below).
The levels are divided into six pages, each containing four stages. The stages are numbered by difficulty (1-4), and the choice of which level to play is made individually for each page. However, the availability of each difficulty level is based to some degree on the player's performance in the last-played stage. Each stage has three collectible hearts, and the number of hearts collected determines the highest level they will be allowed to choose on the next page, adding one to the amount collected. For example, if the player collects two hearts during a stage, they will be allowed to choose from difficulty levels 1, 2 and 3 on the next page.
Yoshi's Story borrows the basic elements of Super Mario World 2: Yoshi's Island. Yoshi can jump, swim, eat things or collect items with his tongue, hold enemies in his mouth, lay eggs from enemies held in his mouth, throw eggs, and hover for a few seconds. However there is one difference from Yoshi's Island: permadeath, and the game cannot be saved to continue with - or rather, all saved data is erased at Game Over.
Source: Wikipedia, Yoshi%27s Story , available under the CC-BY-SA License.