The stork is carrying Baby Mario and Baby Luigi to their parents when Kamek the Magikoopa attacks, knocking the babies away. Baby Mario falls down and onto the back of Yoshi. What happens next, depends on the game mode:

In Score Attack mode, Yoshi will carry Baby Mario to meet the stork at the end of the level. If the player scores 300 points in Score Attack mode, Baby Luigi will be on the back of the stork.

In Marathon mode, Yoshi carries Baby Mario as far as possible, and will hand him over to one of his cousins (other Yoshi) every 1000 yards (in North American versions of the game; other versions use metres). If the player makes it at least 3000 yards without dying, the stork will swoop in with Baby Luigi at the end.

In Time Attack mode, Yoshi and Baby Mario will try to shoot down the Toadies that are carrying Baby Luigi away. The clouds the player draws in this mode are yellow rather than white, causing Yoshi to run faster on these clouds than on the ground.

In Challenge mode, Yoshi and Baby Mario will try to get as far as they can before Kamek the Magikoopa catches them.

The game begins with three different gameplay modes: "Score Attack", "Marathon", and the "multiplayer vs. mode". Additionally, the player can unlock "Time Attack" and "Challenge modes" by getting the high score in the "Score Attack" and "Marathon" modes. When the high score on the two new modes is achieved, the mini-game "Balloon Trip" is unlocked. There are two basic level types. A vertical level, where the player must lead Baby Mario through the sky safe to the ground and a side-scrolling level, where the player takes control over different Yoshis, carrying Baby Mario on their back.

Different from the earlier Yoshi games, in Yoshi Touch & Go the player cannot take direct control over the characters. Instead, the Yoshis move from the left to the right automatically in a certain speed. However, the player can draw lines on the lower screen with the stylus, what creates clouds that will support a character. This attribute allows to create alternate routes to avoid enemies and obstacles. If the drawn clouds are impeding the progress, they disappear by blowing into the microphone. Enemies can be dispatched by drawing circles on them, which puts most of them into a bubble. In the side-scrolling level, a Yoshi can make an egg out of a caught enemy by leading him to its mouth. By tapping on the screen, the Yoshi will launch an egg in that direction, which is useful for killing enemies or collecting coins and fruits. By tapping on a Yoshi himself, the player can make him jump, and tapping him again while he's in midair will cause him to do a flutter-kick jump.

The Nintendo DS's two screens act as one tall screen, whereas the player can only create clouds on the lower one. However, by throwing eggs in the upper screen it is possible to collect coins or fruits from there. An exception provides the wireless "multiplayer vs. mode", where only the lower screen shows the player's view, while the upper screen shows that of the enemy. In the multiplayer, the goal is to be faster than the enemy. By clearing out enemies on the own screen, the player can cause spiky obstacles on the opponent's screen.

In some modes, there is a star point counter. Once this reaches 100, a Super Star will appear. If Yoshi touches it or the player drags it to Yoshi, Baby Mario will temporarily become Super Baby Mario, who is considerably faster than Yoshi and has unlimited stars (instead of eggs) to throw. The star points will then return to zero. Also, by feeding fruits to Yoshi a certain amount of eggs will be replenished. The number of replenished eggs consists of the fruit (for instance, an apple only refills one egg, while melons refill twenty).

The colour of Yoshi that Baby Mario rides depends on his score in the vertical falling part of the game. If he gets 60 points, he will ride a sky blue Yoshi, and then the colour will go up a level for every other 20 points he gets (for instance, pink Yoshi at 80 points, blue Yoshi at 100 points, etc.). The only two exceptions are white and orange Yoshi: In Marathon mode, when Baby Mario changes Yoshis, depending on his performance he might start riding a white Yoshi, who will switch to black Yoshi, unless it's at the 10000 metres mark, in which case he will switch over to orange Yoshi. It will then switch to purple yoshi at 20000 metres in Marathon. In challenge mode, after the high score is beaten, getting 0 points in the Baby Mario segment of future games will unlock a fast purple Yoshi. The same thing applies to time attack where you can also get a white Yoshi, which has unlimited eggs.