The following Orchard documentation should help -
Follow the steps in the section titled 'Upgrading an Orchard Site In-Place'.
Adding App_offline.htm will effectively take the Orchard application offline - any browser request will simply get the contents of App_offline.htm.
This will give you time to ftp all the new files to the website - then deleting App_offline.htm will restart Orchard.
Of course you should take a copy of App_Data and test the databases and settings with a local install of the new version Orchard first to be sure you will not run into any problems upgrading - note the instruction on deleting App_Data/Dependencies.
Other problems you may encounter will be to do with write permissions on various directories, App_Data, Media, Modules & Themes - the latter two to install from the Gallery, but you can download the .nupkg files locally and unzip and then ftp the contents
to your website.