WEB data

I realize that processes such as web page scraping and web data extraction are often left to other micro platforms supporting high level languages such as python and PERL.  But I have seen some older arduino projects which pulled a very small amounts of data, one for stock data, one for weather, one for twitter keywords, occasionally using Json but not always.  I would like to better understand a simple process for pulling data from a server or page either via an API or scraping. Probably suited for WIFI connected ESPs but it would be fun and interesting adding WIFI to the UNO.  Some of these projects use simple LEDs to warn of trends.