You can get the new Twitter API live at Developer.twitter.com.But one thing is that you should have a multi cluster of node else single cluster may hamper in distributing analysis.If you use that single cluster, you should upgrade your Ram memory as well as the virtual memory
There are several tutorials on how to use the Twitter API (just google twitter API tutorial and you will get many results). Of course it also depends on which programming language you use (Python, PHP etc.)
Here is an example with a step by step walkthrough:
node.js easy a easy and powerful scripting language for playing with twitter APIs . I am using node.js. If you are good in coding it will be a pan cake for you.