@jameshowdoi shows how to quickly set up Constraints so characters can grab, hold, and drop objects in an animation.
Some rigs will have controls to pick up, hold, and drop objects, but not all do. Setting up the Constraint for that kind of thing is easy enough, but there are little caveats you need to know to animate pick-ups and holds effectively.
Here, @jameshowdoi shows how to set up a Parent Constraint in Maya and how to set keys for it so you can animate a character picking up, grabbing, holding, dropping & throwing objects.
More on Creating Constraints for Character Rigs.
A little while ago, Andrew Silke covered constraints for animators by looking into working with referenced rigs in Maya, showing methods for using constraints to step in where parenting can’t. Visit that tutorial here.