One of the easiest and most common ways is to use 3D foam adhesive. This layout shows two elements with foam adhesive. A select few clouds are raised up with some foam adhesive squares. The butterfly comes with a foam adhesive already attached.
Adding dimension with handmade flowers is another popular technique. This flower is created with a 1" strip of paper folded in half and rolled. This photo gives an idea of the dimension on the flower and the foam adhesive under the clouds and butterfly.
This adorable flower is simple to create! Use a flower punch on your pattern paper and roll each petal towards the back. I use the end of a paintbrush to roll my petal back and use my fingernail to "loosen" up the roll. Buttons and twine are easy ways to finish off the flower.