This question has been answered by iusemodx. See the first response.
As this is not CMS specific:
My take:
1) Download a copy of the current website
2) Download a copy of the current database
3) Set-up a SUB domain: dev.domain.com
4) Upload the "latest" version of the cms you are using to the dev server
5) Create a second database and import the copied database
6) Start the update: dev.domain.com/install/
You will need to upload the old config file(s), but change the settings in it / them for the new database and for Revo I think you also need to change paths in one or two files, otherwise you will possibly overwrite old stuff
Points 1 + 2 also act as a full backup
