Watch for Patterns
Throughout Sniper Elite, you will be tasked with eliminating particular targets without being spotted. Later in the game, this can be quite difficult, but if you are patient, you can take them down, then slip away into the shadows. Every character has set patterns for each stage, and while some of these patterns may take a bit to play out before repeating themselves, if you are patient and wait the game out, you will see your chance to take the takedown shot.
Camouflage
As you can imagine, every level has its own specific layout, and these stages also offer the player many different hiding spots from where to set up and take their shot. While you have several potential locations, there are a few that are better than others. An easy way to know which spots are good and which ones aren't so much is to keep an eye on your camouflage meter. This can give you a good idea of how well you're blending in to your surroundings and staying out of the eyes of the enemy.
An easy way to conceal yourself in a pinch--say if you're trying to avoid detection in a hurry--is to duck into the shadows. Because these areas are almost always otherwise in the open, they don't make great sniping locations, but if you're at risk of being detected, they are decent hiding locations.
When All Else Fails...
When you have run out of options and there is simply no alternative, there is still one thing you can do: cheat. Sure, it's not exactly "honorable", but this is war and you win by any means necessary in war. There is one cheat code that can give you a definite advantage, and two more that are just kind of fun to play around with.
At the beginning of the game, set your profile name as "Stealth". to make your sniper rifle fire silently, essentially making you invisible.
If you want to make your shots do extra damage (and make them extra loud), enter "Panzer" as your profile name. This makes your bullets explode, as though they were shot from a tank.
Use the profile name "Ratbomb" to make rats explode when shot.