Basically, you need to start from a feed. If you don’t have a feed provided, then you can scrape to a feed, in effect creating your own feed. Some websites will give you a feed of their search results; otherwise, you need to filter the feed yourself.
IFTTT is currently listing 39 Recipes for Mashable, including “RSS feed Mashable on Twitter”.
IFTTT currently lists 7 Recipes for TheVerge, including “Get new feed item from theVerge and post as the new tweet for your followers”.
is an online forum dedicated to Twitter bot enthusiasts. I have aggregated many recent articles on Scoop.it about , which detail various and sundry methods.
See also my quick and dirty webpages: