If you don't have a Pocket account, goto getpocket.com and sign up. And download the Pocket app or gadget for any of your devices listed in the website. (I am using iPhone app here)
Pocket app in iPhone
The two articles I have already added from my browser to pocket.
Now, in twitter goto settings (I am using twitter app in iPhone)
Scroll down and look for 'Services' and choose Read Later
Type in your pocket username and password
Now pocket is Read Later service in twitter
Now for example, if you want to read the article tweeted by Verge.
Swipe on the tweet and choose the 'more' option and just choose 'Read Later'
Now, that article is automatically downloaded to the Pocket app.
This is how the article is shown in the pocket app