• make sure, you are running on SQL Server 2005 or 2008 (and your database is not in SQL server 2000 compatibility mode)
• make sure having .Net framework 3.5 SP1 installed
• DNN 5.2.0 has a bug with non-ASCII characters like German umlauts, ç, kyrillic and asian characters. if you use it, I suggest waiting for 5.2.1
• to upgrade:
  • backup all files and database
  • stop the website or at least turn off AutoUpgrade in web.config (edit with a text editor)
  • download upgrade package and unzip files hierarchically into DNN installation folder
  • start web site
  • if autoupgrade turned off, browse to /install/install.aspx?mode=upgrade to trigger upgrade
  • review the upgrade log on the screen
  • if it went well, go to Host :: Extensions to upgrade modules. HTML should be upgraded automatically, form and List is successor of UserDefinedTable and will keep all data. New versions of Forums, Reports and other modules are included as well.

the description on download page is not up2date, upgrade packages do include latest module packages since ~DNN 4.9,0

Module upgrades are not installed automatically during upgrade (except Text/HTML), you need start upgrade in Host :: Extensions, using "install available extensions".

DNN 5.2.1 will be monthly release for December.