In Code

XAML (preferred)

<ContentPage x:Class="...">
  <ContentPage.Resources>
    <StyleSheet Source="appresources/style.css" />
  </ContentPage.Resources>
</ContentPage>

the Source argument takes an Uri relative to the current xaml control, or relative to the application root if it starts with a /. The style.css has to be an EmbeddedResource.

alternatively, you can inline your style in a CDATA Section

<ContentPage x:Class="...">
  <ContentPage.Resources>
    <StyleSheet>
<![CDATA[
^contentpage {
    background-color: orange;
    padding: 20;
}

stacklayout > * {
    margin: 3;
}
]]>
    </StyleSheet>
  </ContentPage.Resources>
</ContentPage>

do not abuse of that second syntax.

in C

From an embedded resource:

myPage.Resources.Add(StyleSheet.FromAssemblyResource(this.GetType().Assembly, "resource.id.of.the.css"));

or from a TextReader:

using (var reader = new StringReader(my_css_string))
    myPage.Resources.Add(StyleSheet.FromReader(reader));

StyleSheet, XamlC and other potential optimizations

At this time, CSS StyleSheets are parsed and evaluated at runtime. That aren't compiled. Every time a StyleSheet is used, it's reparsed again. If parsing time is an issue, enabling caching is trivial, but comes at memory cost.