Using Blueprint's Play Montage Node
You can call the Play Montage node within Blueprint (below we tell a Skeletal Mesh called Mesh to play a Montage when the character is clicked on with the Left Mouse Button).
The Play Montage node enables you to not only select what Montage to play but you can also set the Play Rate, Starting Position and Starting Section as inputs.
On the output side, there are several callback events that you can use to trigger other script based on the state of the Montage:
On Completed - called when the Montage finishes playing and is fully blended out.
On Blend Out - called when the Montage is starting to Blend Out, using Blend Out Trigger Time or if the Montage ends.
On Interrupted - called if the Montage is starting to Blend Out, due to interruption by another Montage.
On Notify Begin and On Notify End - are callbacks when using either Play Montage Notify or Play Montage Notify Window Anim Notifies in the Montage asset.
In order for the Montage to play, the Skeletal Mesh will need to have its Animation Mode set to Use Animation Blueprint and the Anim Class pointed to an Animation Blueprint.
Inside your Animation Blueprint, on the AnimGraph, you can use the Slot node to define which Slot from the Montage you want to play.