It's simple, and there are multiple ways of doing it :
1) When viewing an article that is beyond your 20 article-pre-month limit, simply erase the numerical paywall code in the URL, and hit reload - Voila¡ ;
2) Sign in as a different user - for example as a Gmail user;
3) Simply Google "Hoe To Beat NYT Paywall". for many other ways to get through this cheap forty million dollar chain-link fence.