After signup, create an app to get API Key, API Secret, Access Token and Access Token Secret.
Before creating API Key and API Secret, apply for elevated access (otherwise we can only do limited things with the API, posting tweets is allowed only with elevated access. You can easily get elevated access if you don't plan to develop for any government organization.)
Setup User Authentication Settings.
Use Read and write and Direct message for App Permissions.
Use Web App, Automated App or Bot for Type of App.