Either install the NuGet package and reference the resource dictionaries in the App.xaml file of the consuming application, or install the package and reference the same resource dictionaries in the control itself in the library:
<UserControl x:Class="WpfControlLibrary1.UserControl1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:local="clr-namespace:WpfControlLibrary1"
mc:Ignorable="d"
d:DesignHeight="450" d:DesignWidth="800">
<UserControl.Resources>
<ResourceDictionary>
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="pack://application:,,,/MaterialDesignThemes.Wpf;component/Themes/MaterialDesignTheme.Light.xaml" />
<ResourceDictionary Source="pack://application:,,,/MaterialDesignThemes.Wpf;component/Themes/MaterialDesignTheme.Defaults.xaml" />
<ResourceDictionary Source="pack://application:,,,/MaterialDesignColors;component/Themes/Recommended/Primary/MaterialDesignColor.DeepPurple.xaml" />
<ResourceDictionary Source="pack://application:,,,/MaterialDesignColors;component/Themes/Recommended/Accent/MaterialDesignColor.Lime.xaml" />
</ResourceDictionary.MergedDictionaries>
</ResourceDictionary>
</UserControl.Resources>
<Grid>
<Button Style="{StaticResource MaterialDesignRaisedAccentButton}"
Content="Test"/>
</Grid>
</UserControl>
Make sure that the MaterialDesignThemes.Wpf and MaterialDesignColors assemblies are copied to the output directory of the app when you build:
Dependent DLL is not getting copied to the build output folder in Visual Studio