I am new to JSF world. I am using JSF in Action book for JSF reference.
In their Custom Component Development chapter, they have created a custom component UIDateInput.
This component creates three html select option tag pairs filled with month, year and day parts of a date.
The easiest way to do this is to subclass an existing component that already has these features.
Just as a warning, however, creating a custom JSF binary component is something you should only attempt as an absolute last resort. JSF components started out as an extended JSP tag construct but they quickly got lost and the results these days are a mish-mash resulting from blending about 3 different and occasionally conflicting concepts, with documentation that's generally poor and out of date. For most cases, it's a lot easier to build components at the XML source level instead.
An IDE is no substitute for an Intelligent Developer.