The easiest way to learn sniper spots and routes is to offer a hand to a sniper, "I'll cover you on your route out." Now you can learn a sniper's route, first spot, and see where he engages other snipers at.
A personal story: I offered a sniper cover on his route, and as he was moving, he used the same exact points on the ground that I used. Through the river, up a small hill, turn on the dark colored spot near top of hill, down to valley etc. It told me that my routes and movement were very similiar to his, and that ambushing him would be easier the next time we played.
Another personal story: One sniper was always really hard to find until he got onto position. So I offered to cover his routes. He took the ugliest and most reckless routes to get out to his spots. Moving across open areas, close to the opponents spawns, and disregarding all of the standard protocols for sniper movement. It was easy to figure out why it was hard to spot that sniper, because he moved where no other sniper would.
On every map, take a few minutes to just drop in a covered position, look at the overall map view, and see where the snipers move. A few minutes of doing this when you first start playing a game will add a lot of enjoyment later on, when you know where the snipers will be, how they will get there, and how to counter them.