Do you mean you want to upload the file to your (or someone else's) Web host or do you want to interact in some way with a Web page which is expecting its users to upload files through it?
If the former, you would do it manually using CPanel or FTP. If you want to automate the process, then I think the easiest way is to use FTP. I've used Stuart McCall's FTP Client very succesfully: it's quick and easy to install and it appears to works completely reliably.
(1) You can upload a file en bloc to a Web server using FTP, so you could for example write some worksheet cells out to a CSV file and then use FTP to upload that file to a Web server provided you have access to the server. If you're doing this every time the workbook is used you're going to end up with multiple files on the server so some method of avoiding duplicated names will be required. What happens to the files once they're on the server is another question.
Stuart McCall's FTP package can handle all of that very neatly.
(2) If you want to add data from your worksheet to an actual database on a Web server, you need to understand what the database is (MySQL?), where it is and what methods you have at your disposal for adding data to it.
Typically you would write a PHP script which runs on the Web server and which is capable of interacting with a MySQL database using SQL commands, and you would invoke the script directly from your Web browser, passing any authentication information and the actual data to be stored to the script at the same time. The term commonly used for this technique is 'server-side scripting'.
(You may have seen URLs where the Web page's name ends with .php? This is a PHP script which sits on and runs on the Web server and you are invoking it from your Web browser. The list following the ? and separated by & are the data which your browser is sending to the PHP script.)
Not all Web hosts offer PHP and MySQL, so you'd need to check that.
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Do you know which of these two options you want?