The intro level of Yoshi's Island is a short sequence of text boxes that can be advanced and then Start + Select can be used to exit the level. Switching to hasty is mandatory. Also see button mashing regarding all level intros.
1-1 is widely accepted to be one of the more difficult levels, even though it is the first it features many mechanics that will be used for the rest of the run so get ready for some fun!
Optimally you eat the Dayzee and do a neutral into the Piranha Plant as you can see in the tutorial video linked at the bottom of this page, and gif below. Then you jump onto platform then Yellow Shy Guy as to avoid a bad screen scroll and do an extended flutter up to the left to the lower platform. Swallowing the Shy Guy during your reflutter is a good strat, but the Shy Guy must be swallowed. See Making Eggs for more info on swallowing enemies. Once you have reached the platform jump up to the second platform grab the Flower. After grabbing the Flower jump left and grab the Fly Guy trying to collect all Stars. Jump up to the second platform and grab all Red Coins which are in the middle row of coins.
Jump off the end of the platform as you see in the tutorial video and do a back tongue to grab the yellow Shy Guy. Then proceed under the Piranha Plant to the pipe while swallowing the enemy with a small jump.
As you enter the cave section begin moving right falling down onto the Egg Block. Jump off the Egg Block and eat the Fly Guy collecting the Red Coin. Tongue the Green Shy Guy, and upspit it into the Red Fly Guy collecting the Red Coin. Immediately after landing begin a horizontal egg shot to collect the three Red Coins to the right. After your shot go back to the left and collect the Red Coin on the ground. Quickly after begin an upshot and when your Egg Cursor is on the coin hanging from the Balloon release the shot to collect the three Red Coins above you. As the Egg ricochet's, proceed to jump onto the brown chomp rock, once the Egg has changed into a Red Egg tongue the Egg to get it for later. Proceed up to the pipe and back to the first screen. See Red Eggs for more info on Eggs and Egg making. The gif below demonstrates the Cave Screen at normal speed.
Screen One Pt.2
First thing after coming up from the pipe up tongue the Yellow Shy Guy above Yoshi before you jumping. Then proceed to the right tonguing the Green Shy Guy do a quick neutral into the white rock it will ricochet down and collect the Flower below. Jump to the white rock you just Egg'd at and jump over the Piranha Plant. Begin an Egg Shot when level with the Piranha Plant, and lock it when horizontal. Be careful here with this Egg shot as getting a Red Egg to hit the Piranha Plant will cause lag. Move left once you land on the platform and shoot the Egg to collect the Red Coins. Collect the Flower with Yoshi. See the gif below for a demonstration.
Then proceed up the pinwheel platforms jumping over the arrow sign to land on the lower hill. Jump and aim an Egg, when it is at the correct angle to hit the cloud release the shot and flutter through the cloud. As you land on the white rock jump and upspit the Shy Guy while moving right it will land behind you. As you move right against the wall a cloud will spawn as you touch it, an up Egg will open the cloud. Collect all the Stars. Jump onto the Shy Guy doing an Extended Flutter up grabbing the Flower collect a Star or two if you can. Land on the rock and jump up onto the pinwheel platforms. A left-right here can help to position you to collect to the two Red Coins above. See the gif below for a demonstration.
Land on the white rock and jump to the yellow grass and over the chomp rock landing just in front of the Green Shy Guy tongue and immediately spit it out killing the Piranha Plant, letting go of right can slow you just enough to execute this correctly. Tongue the Red Shy Guy and jump skipping the very steep slope. During the jump begin and egg shot and when you land jump again immediately your egg cursor should be aimed at the winged cloud, and swallow the Shy Guy. Land on the flat spot of the white rock jumping through the cloud collecting all Stars. As you land tongue the Pink Shy Guy, and jump on the top of the last two hills. Then proceed to do the Zewing Skip.
1-1 100% Commentated Tutorial
Below is a commentated version of what is described here in text and should be watched along with this text.