First the theme stylesheet needs to be accessible by Tiki. There are a couple of ways to do this.
To be listed in the "Theme" selector on the Look and Feel admin page (tiki-admin.php?page=look), the theme must be placed in tikiroot/themes/mythemename/css/ directory (which of course must be made first) and have the name mythemename.css. Any related files should be placed in appropriate subdirectories under the mythemename directory. (See the file hierarchy description at Tiki's CSS and Smarty template organization.)
On the Look and Feel admin page, in the "Site theme" selector, choose "Custom theme by specifying URL". Then input the stylesheet's URL in the "Custom theme URL" field. This can be either an absolute URL or a relative IRL from the Tiki root, or even a file gallery download link (? check this). So you can test a theme stylesheet by "hot-linking" to it on another server (not recommended for production use).
How the theme is used can be configured in a few ways. It can be set for all pages of the site including admin pages, or just admin pages, or all pages except for admin pages. It can also be set to be used only for a particular feature, like blogs, or content category, or user group, or perspective (perspectives are a collection of site preferences).
There is also a "Custom CSS" textarea under the "Customization" tab of the Look and Feel admin page where CSS rules can be entered. This may be convenient for site-specific rules such as for a particular page (all wiki pages have a unique body element, for example). Or for temporary adjustments that will eventually be moved to the stylesheet itself.
Or if the theme is good for most pages, etc. but a variation would be good for some, then an easy solution is to make a theme option. This is a "child" stylesheet that has rules to overwrite some of the parent's rules, such as to modify the color palette. In this case, make the CSS file and place it in the theme's directory, in a subdirectory named "options". (Check the file hierarch here: .)