You already know file types and the best file for the situation, and now, we will briefly introduce how to export files in Photoshop, and after that, you will have needed to learn everything for the Adobe Certified Associate exam, most of it at least.

All exporting takes place under File > Export. There are 3 main options for export:

Quick Export as .png
Export As
Save for Web(Legacy)

Export As:

This is the easiest way to export an image. You can choose your file type and basic settings. For a more complex method of exporting, "export for web" would be a better option.

Save for Web

This is the best option for a more diverse method of exporting. This allows for more customization and Ctrl over the final file.

Printing can also be done by going to File à Print, or Ctrl/Command+P.

Be sure to pay attention to what the client needs as the final product in terms of File Type!