Twitter has two ways of identifying accounts, an @username that a user chooses and can change, and a Twitter ID that is permanent. The @username can present a problem of link rot over time as users change their handle, so sometimes linking directly to the Twitter ID is preferred.
The first step is to get the Twitter ID from the current @username. Let’s use @CNN as an example. There are a few websites that do the conversion, but these sites seem to break from time to time. One that currently works is GetTwitterID.com.