In your case extract the archive, and you will have "coral_reef" folder with some files. You should upload the folder "coral_reef" and its content in to themes folder of your XOOPS site. Be shure you do not have duplicate folder names there and if you have rename one of the folders!
Once uploaded, you have two options.
- If you run muultitheme site: go in admin -> preferences -> general and in "Selectable themes" select your new theme which will be "coral_reef" in this example.
After doing that the theme will be selectable in the "theme select" block. (You can enable/make visible this block in the blocks menu and after thatin the groups menu you shuld give access to this block to groups you whant)

- your second option is to select the new theme as default in admin -> preferences -> general "Default theme" dropdown box. and confirm the new settings. (if you go this way, I suggest that you keep this browser in admin, open new browser and access your site to see if the theme is compatible. If it is not, you may have a blank screen and then use the first browser to change the default theme to old one)

Sorry if I don't explain it clear in english...