Researching Opponents
You should be able to research their games in their history. Under the "Ratings" chart, just click the highlighted number next to "Total Games" to see the player's games. In your case, for example, by clicking the number ["13"] next to your Online games, I can see your previous games.
I'm new to classical length otb rated chess. I frequently see posts on this site in which the poster casually mentions going over his prior opponent's games before the match to prepare. How does one find such information? The players against whom I have played so far were all fairly low-rated (1550, 1580, and 1650) so their games weren't on any major sites naturally, but I frequently see posters researching opponents even lower rated than that. Just, how?