In this Redstone tutorial, you will need:
2 Regular Pistons,
1 Sticky Piston,
2 Slime Blocks,
1 Boat or 1 Minecart and Rail,
and 2 Redstone Blocks.
Step 1) A few blocks off the ground (or more if you're feeling ambitious), place 1 piston and one sticky piston back to back. The normal piston should be facing the way you want your plane to go.
Step 2) Place the slime blocks either side of your pistons. So far, your plane should have 4 blocks going in the order : Slime block, Sticky piston, Regular Piston, Slime block.
Step 3) On top of both of the Slime blocks, place the redstone blocks. Now, it should be in a bit of a U shape.
Step 4) Now place your boat or minecart so it goes on top of the pistons.
Step 5) Finally, put your last piston so it pushes the slime block attached the sticky piston and then you can get in and ride!
If you want to, you can add extra blocks on the sides of the Slime to make it look a bit more like a plane - or you could take the idea further and make a humongous slime robot like the one featured in our Top 3 Redstone Creations list.
If you want a video tutorial, try one of these:
https://www.youtube.com/watch?v=WeQMXuXP-JM
or
https://www.youtube.com/watch?v=X9ABSf1Y0NQ