I am interested in help with making my font looking like the image I have downloaded. I have made text in illustrator using glyphs, but am having a hard time figuring out how to shape it.
This type of distortion can be made using an envelope mesh.
Begin with some ordinary text or any grouped artwork, and in the main menu click
Envelope Distort >
Make with Mesh
Set to 1 row and 1 column, hit OK. Then you can use the Direct Selection Tool (A) to select the corner anchors, move them, and to adjust the curve handles to create the kind of curve you want.