The simplest of the five trigger types, the Trigger is responsible for setting properties based on other properties within the same control.

<TextBlock>
    <TextBlock.Style>
        <Style TargetType="{x:Type TextBlock}">
            <Style.Triggers>
                <Trigger Property="Text" Value="Pass">
                    <Setter Property="Foreground" Value="Green"/>
                </Trigger>
            </Style.Triggers>
        </Style>
    </TextBlock.Style>
</TextBlock>

In this example, the foreground color of the TextBlock will turn green when it's Text property is equal to the string "Pass".

A MultiTrigger is similar to a standard Trigger in that it only applies to properties within the same control. The difference is that a MultiTrigger has multiple conditions which must be satisfied before the trigger will operate. Conditions are defined using the <Condition> tag.

<TextBlock x:Name="_txtBlock" IsEnabled="False">
    <TextBlock.Style>
        <Style TargetType="{x:Type TextBlock}">
            <Style.Triggers>
                <MultiTrigger>
                    <MultiTrigger.Conditions>
                        <Condition Property="Text" Value="Pass"/>
                        <Condition Property="IsEnabled" Value="True"/>
                    </MultiTrigger.Conditions>
                    <Setter Property="Foreground" Value="Green"/>
                </MultiTrigger>
            </Style.Triggers>
        </Style>
    </TextBlock.Style>
</TextBlock>

Notice the MultiTrigger will not activate until both conditions are met.

A DataTrigger can be attached to any property, be it on it's own control, another control, or even a property in a non UI class. Consider the following simple class.

public class Cheese
{
    public string Name { get; set; }
    public double Age { get; set; }
    public int StinkLevel { get; set; }
}

Which we will attach as the DataContext in the following TextBlock.

<TextBlock Text="{Binding Name}">
    <TextBlock.DataContext>
        <local:Cheese Age="12" StinkLevel="100" Name="Limburger"/>
    </TextBlock.DataContext>
    <TextBlock.Style>
        <Style TargetType="{x:Type TextBlock}">
            <Style.Triggers>
                <DataTrigger Binding="{Binding StinkLevel}" Value="100">
                    <Setter Property="Foreground" Value="Green"/>
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </TextBlock.Style>
</TextBlock>

In the preceeding code, the TextBlock.Foreground property will be Green. If we change the StinkLevel property in our XAML to anything other than 100, the Text.Foreground property will revert to it's default value.