This post assumes that you already have the Cinnamon shell installed on your computer and you want to install new Cinnomon themes for your personnal use rather than for global use.
If you do not already have a ~/.themes subdirectory, you need to create it. The default permissions are fine.
You can either use the Cinnamon Settings tool (Menu->Preferences->Cinnamon Settings) to preview, select and download a new theme, or you can download a theme directly from here.
Themes files are compressed and packaged as a single zip file. Move the downloaded zipped theme file to ~/.themes and unzip it. A new subdirectory named after the theme will be created. For example, if you download the Smooth Mint theme, a subdirectory called ~/.themes/SmoothMint is created. Within that subdirectory, a subdirectory called cinnamon is created and this is the subdirectory that contains all of the actual theme files. For example, here is what is created for the SmoothMint theme.
[SmoothMint]$ ls -R .: cinnamon ./cinnamon: calendar-arrow-left.svg panel-button-border.svg calendar-arrow-right.svg panel-button-highlight-narrow.svg calendar-today.svg panel-button-highlight-wide.svg cinnamon.css player-paused.svg cinnamon.css~ player-playing.svg cinnamon.css.old player-stopped.svg close.svg process-working.svg close-window.png running-indicator.svg close-window.svg scroll-hhandle.svg corner-ripple-ltr.png scroll-vhandle.svg corner-ripple-rtl.png source-button-border.svg dash-placeholder.svg thumbnail-generic.png filter-selected-ltr.svg thumbnail.png filter-selected-rtl.svg toggle-off-intl.svg gdm.css toggle-off-us.svg menuold.png toggle-on-intl.svg menu.png toggle-on-us.svg overview-hover.png ws-switch-arrow-down.svg overview.png ws-switch-arrow-up.svg panel-border.svg [SmoothMint]$
You can then use the Cinnomon Settings tool to select the new theme. Once selected, the new theme is immediately visible; there is no need to log off and log back in again.