One style, applied implicitly, that turns WPF's tooltip into a flat bordered card in the theme colours and fades it in and out.

<Button Content="Save" ToolTip="Save the current document" />
Styles/Controls.xaml applies MahApps.Styles.ToolTip to every ToolTip, so the quick start is all the setup there is. There is no second style and no variant.
What the style sets
| Property | Set to |
|---|---|
Background |
MahApps.Brushes.Control.Background |
BorderBrush |
MahApps.Brushes.Gray7 |
BorderThickness |
1 |
Foreground |
MahApps.Brushes.ThemeForeground |
FontSize |
MahApps.Font.Size.Tooltip, which is 12 |
Padding |
6 3 |
SnapsToDevicePixels |
True |
All seven are ordinary properties on a border the template draws, so all seven can be changed on the control:

<Button Content="Save">
<Button.ToolTip>
<ToolTip Content="Save the document"
Background="{DynamicResource MahApps.Brushes.Accent}"
BorderBrush="{DynamicResource MahApps.Brushes.AccentBase}"
Foreground="{DynamicResource MahApps.Brushes.IdealForeground}" />
</Button.ToolTip>
</Button>
Note what is missing: the template's border has no CornerRadius binding, so a tooltip is always square-cornered — ControlsHelper.CornerRadius does nothing here, unlike on a Label or a Button. There is no drop shadow either.
Both are already fixed in develop and will arrive with the next release: the border gets CornerRadius="{TemplateBinding mah:ControlsHelper.CornerRadius}", and a HasDropShadow setter — True by default — applies a new MahApps.DropShadowEffect.ToolTip. Until then, rounding a tooltip means replacing the template, and if you do, mind the visual states below.
The fade
The template's root border is written as Opacity="0", and an OpenStates visual state group fades it to 1 over 0.3 seconds when the tooltip opens, then back to 0 over 0.4 on close.
That means a replacement template must keep those visual states. Drop them and you get a tooltip that is measured, positioned and completely invisible — with no error to tell you why. If you write your own, copy the VisualStateManager.VisualStateGroups block across with it, or start the root at Opacity="1" and give up the fade.
Content
The template's presenter is a mah:ContentControlEx, which is what makes ControlsHelper.ContentCharacterCasing work on a tooltip:

<ToolTip Content="Save the document" mah:ControlsHelper.ContentCharacterCasing="Upper" />
Being a ContentControl, a tooltip is not limited to a string. ContentTemplate and ContentStringFormat are template-bound, and anything you put in the content is laid out normally:

<Button Content="Save">
<Button.ToolTip>
<ToolTip>
<StackPanel MaxWidth="220">
<TextBlock FontWeight="SemiBold" Text="Save" />
<TextBlock Margin="0 2 0 0"
TextWrapping="Wrap"
Text="Writes the current document to disk. Ctrl+S does the same." />
</StackPanel>
</ToolTip>
</Button.ToolTip>
</Button>
A tooltip does not size itself, so give a wrapping block a MaxWidth or a long sentence turns into one very long line.
Timing and placement
None of this is MahApps — the style changes how a tooltip looks, not when it appears. That stays with WPF's ToolTipService, and the library sets no defaults for it:
| Attached property | WPF default | |
|---|---|---|
InitialShowDelay |
system, ~1000 ms | how long the pointer has to rest first |
ShowDuration |
5000 ms | how long it stays; raise it for anything worth reading |
BetweenShowDelay |
system, ~100 ms | grace period in which the next tooltip appears at once |
ShowOnDisabled |
False |
set it to show why a control is disabled |
Placement, PlacementTarget |
Mouse |
<Button Content="Save"
IsEnabled="False"
ToolTip="Nothing to save yet"
ToolTipService.ShowOnDisabled="True"
ToolTipService.ShowDuration="20000" />
ShowOnDisabled is the one worth remembering: a disabled control with an unexplained reason is exactly where a tooltip earns its keep, and by default it will not show one.
Related
Slider and RangeSlider have their own value tooltip through AutoToolTipPlacement, which is a separate mechanism and does not use this style. Validation errors are drawn by CustomValidationPopup rather than by a tooltip — see Validation.