Look through the Dynasty stories and see the kinds of shots that players take. Pam is renowned for her screenshots so that's a good starting point. She's taught me a lot simply by me paying attention to how she does things.
If there's one piece of advice I would give it's
get close. Fiddling with the camera can be a pain to get the exact angle and distance you want, but you do want to be pretty close. A Sims' expression isn't really obvious unless you're pretty close anyway—and good expressions really can make the difference between a so-so screenshot and a good screenshot.
The vast majority of screenshots on the forum are run-of-the mill screenshots...and I'll be the first to raise my hand in supplying many of those.
So, get creative. Think of showing a Sim going into labor from different angles. And there's nothing wrong with
staging set-ups. What I mean is creating special situations/placements just for the screenshot. Heck, the vast majority of my Dynasty photos are examples of that technique — i.e. moving Agnes' ice sculpture around like she's spying on the Sims.
EDIT: I went into my Dynasty game and took two screenshots — both of the same moment in time for my guitarist. The first screenshot below is your standard View My Sim angle — looking down on the action from a medium ranged distance. This is often the orientation I use when issuing commands to multiple Sims in a house because I can see everyone. But, the angle and distance for the screenshot turns this into a ho-hum photo — nothing special.
The photo below is a vast improvement because I got down on eye level and moved in closer to the action. But, honestly I still just rate this as "good" and not "really good" because of the lighting. The fact that this is taken at night with very little available light hides the Sims' expressions. Night shots are definitely good sometimes, especially if you're trying to convey emotion — like a romantic kiss, etc. But, a daytime shot will almost always be better than a nighttime shot because you can simply see more of what's going on.