This page of our guide to Sniper Elite 4 explains how to use silencers and mute ammunition. They can be very helpful in eliminating enemies while remaining unnoticed and are the recommended way to complete the game.
1. Not all the weapons have a silencer. Using such a weapon will alarm nearby opponents and make them look around for a while. If you use your sniper rifle twice in a row, from the same location, opponents will know where you are. They will shoot at you and try to come closer (they may even call for reinforcements).
2. Using a silencer gives you a major advantage. There are some drawbacks - the silencer will significantly decrease the damage (except for headshots [when your opponent does not have a helmet/you hit an exposed part of the body, e.g. face or neck]). When you have the silencer, you use regular ammo to take silenced shots.
3. To improve your skills, use suppressed ammo, which can be selected (if you have any) weapon selection screen. It has the same effect as the silencer. The only difference is that Suppressed Ammo is hard to find.