Question

in developing your own RESTful API. does it necessarilly needed to use the four different http methods? GET POST PUT & DELETE?

i was checking the Twitter REST API and saw that they are just using the common methods (GET & POST)

Answer 1

Short answer: No

Long Answer:
REST is not specific to any one protocol, instead it is a style of programming. This is helpful to keep in mind because a RESTful endpoint should be thought of as having specific goals. Your job is to expose the web service in the most RESTful way possible.
When you’re making a RESTful API you are not required to use any specific HTTP methods. Instead, REST can be embodied in this guiding principal: That you must expose individually identifiable resources; these resources must be manipulable in their exposed form. Oh and use self descriptive messages.

I’m sure this is a leaky explanation. Try to see, though, that REST becomes much more clear when you have the key idea in mind. RESTful practices expose resources in a way that allows us work with state in a sane manner. The technical details of how to implement a RESTful API can be learned by reading this:
http://en.wikipedia.org/wiki/Representational_state_transfer
After that, read something specific to your language. Fast track: find some RESTful API written in your language and clone it/play with it.