I like the series "Art of Crochet by Teresa" and her demonstration of a half granny square seems very simple.
I also like her - Crochet V-stitch Granny Square
Here's some of my "aspiring too" pieces from my antique crochet collection. All were made by my great-aunts and grandmothers. Some still have to be put together.
I have used all of the above at some point. My favorite is the green doily.
During the lifetime of my grandmothers and great-aunts it was fairly common to see crocheted items used round the homes as dresser sets, under vases, to edge napkins, as plate covers, teapot warmers, table runners etc. Surprisingly I have no granny square items in my collection but I do know my grandmother made at least one blanket in her lifetime.