It's easy to do, you have many different options.
For example, here's how you might do it in PHP:
1. Create an HTML form for the user to select the local file to upload.
Specify method="post", enctype="multipart/form-data" and the name of your PHP script on the server
2. Your PHP script will validate the input and call the built-in function "move_uploaded_file()"
3. Voila! File upload accomplished
You have similar options for Ruby/Ruby on Rails, Java/Tomcat, or whatever server-side web platform you prefer.