Instructions
Load "Mass Effect" and open your saved game file. While playing, equip your sniper rifle and use it. You will not be very accurate with it if you have never used it before.
Gain experience points while using the sniper rifle. When you gain a level open the Mission Computer.
Access the equipment screen from the Mission Computer and select the sniper rifle.
Click to view the upgrade screen for the sniper rifle and choose the stat upgrades to which you wish to devote skill points.
Click "Confirm" to accept these upgrades, then exit the upgrade screen.
Pull out the sniper rifle in combat. If you have the required amount of proficiency with it you will be able to use the sniper scope by pressing the left trigger and holding down the right analog button, if you are on the Xbox 360, or by pressing the right mouse button and holding down "E" if you are on the PC.