Generally copying new DNN version over the existing and letting newer files to overwrite old does the trick in most cases. The only critical part is to retain original machine key values in the webconfig and obviously a connection string. Having said that this is not always work correctly especially if you are going from 3.x.x to 4.x.x.
In cases when upgrading from DNN 3.x.x to 4.x.x you will also need to change ASP.NET version from 1.1 to 2.0. In some cases the old modules may fail to load, or you may encounter database schema issues, or other unforeseen problems. Some issues can be worked out with a bit of SQL knowledge and direct database modifications, others may leave you no choice but to keep your original site using the older version.
There is also an option to export your portal and content as template and then applying the template to the new installation. The key here is to have all the original modules already installed and copy the media files manually to the appropriate /portals/[portal_id] folder. This may not work if your modules do not cooperate to emit data in to the template.
In any case, the upgrade process cannot be taken casually and you should always make proper backups prior to attempting it.