How can I recursively find all files in current and subfolders based on wildcard matching?

Use find:

find . -name "foo*"

find needs a starting point, so the . (dot) points to the current directory.

Piping find into grep is often more convenient; it gives you the full power of regular expressions for arbitrary wildcard matching.

For example, to find all files with case insensitive string "foo" in the filename:

~$ find . -print | grep -i foo