Combine find and wc to count files in the current directory and in all of its subdirectories:
find . -type f | wc -l-type f: include only fileswc -l: count lines only
If you remove -type f it will also count directories and symlinks.
Add -name "*.EXT" to count files with the specific extension. In the example below it counts only CSV files
find . -type f -name "*.csv" | wc -l