It depends on what kind of access you have to your server. Some web panels provide an interface to upload and update your files, simply through the web. FTP used to be the most common protocol for transferring files, but it is somewhat insecure and old now. Most seasoned webmasters prefer to use SSH which is very secure and allows you to do pretty much everything. There is a learning curve involved however.
As boltok said, FTP and SSH are two common options. Depending on your host you may also have a control panel that allows you to use a file management tool. I don't really like using it, but the option is there if you need it. FTP or SSH are most likely the solution you'd want to use. If you are using a shared host, I don't think you are provided with the option of using SSH.
FTP is still the common, I doubt many host will give you SSH access, just download a free ftp software for eg http://filezilla-project.org/ it is pretty straightforward to load. Keep in your Host, username and password and here you go!