The Pickers - TimePicker, DatePicker and NumberPicker provide easy to use ways of getting user input without having to use an on-screen keyboard.
Pickers are usually introduced as dialog boxes or dialog fragments. This is a good way to use them, but they are also useful within a general layout.
With the introduction of Material Design with Android Lollipop, the look of the Pickers has changed. For easy backward compatibility use compatibility library v7 appcompat, which is included in your projects automatically by Android Studio, and stick with the AppCompat themes.
If you stick with these defaults your app will use Material Design on Lollipop and later, but the Holo theme for earlier versions of Android.
If you stray from AppCompat themes things tend not to work.
It is possible and very easy to replace the Material Design with the Holo look on all versions of Android. Simply set the timePickerMode and/or datePickerMode properties to spinner. The NumberPicker always shows as a spinner.
Use the OnXChangedListener event handler to respond to user input.
The DatePicker in spinner form can also display a calender using the CalendarViewShown property.
The designer isn't very stable. If it complains about missing classes or styles try ignoring the errors and running the project. This often clears the errors and allows the Pickers to render correctly.
Conclusion
There is much more to say about the Pickers and how to customize them, but the methods explained here are the most common and customization generally only involves the use of fairly obvious properties and methods.
