I've mostly seen two explanations as to why people didn't smile in photos. The first is that it was hard to hold a smile in a photograph. Early cameras had very long film exposure times in which you had to sit perfectly still or else you'd turn out blurry. Some old cameras, like the Daguerreotypes (You can see the Library of Congress's collection of this kind of photo here: http://www.loc.gov/pictures/collection/dag/) had an exposure type of fifteen minutes!

It's much easier to sit perfectly still for fifteen minutes with a blank or relaxed expression on your face then it is to hold a perfect smile on it. Just try it in front of a mirror if you don't believe me. Even if you can manage it, the smile starts looking a little demented as time goes on.

The second reason I've read behind people not smiling in photographs is that early photographs were taken as seriously as portraits. They were serious things meant to be passed down through the family and early ones were expensive to take as well. For example, here's a note from Mark Twain about smiling in photos:

A photograph is a most important document, and there is nothing more damning to go down to posterity than a silly, foolish smile caught and fixed forever.

That all said, your question is when did people start smiling and there's no good answer in my book for that as there's definitely 'old' photos from the 1800s in which people are attempting smirks or smiles far before they became common. Then there's pictures like my grandparent's wedding day where they all look so serious that it could be a funeral but for the wedding dresses. (They were married in 1949.) I would say (opinion) that smiling became increasingly common as the technology improved and costs decreased. Once people were able to move away from formal portraits and take pictures instantly or almost-instantly I think the tendency to take pictures during happy moments where there were already smiles in place would rise. Which in turn would cause more and more people to think you should smile during a photograph. (Which is where you get photos like my parent's wedding in 1983 where it's obvious they're all half-way to drunk.)