Sniper is an extremely long-ranged autoattack-reliant hero. It is crucial to keep your distance from the enemy in any situation. Sniper has no built-in escapes, so the best you can do is rely on items that give you one in some form. This means getting a Shadow Blade and Manta Style. As long as your keep your distance, and use your godly range to harass the enemy at every given chance, you should do fine.

IMPORTANT NOTE (thanks to Dung for reminding me): Get shrapnel before level 6 if you are playing with a Rubick in the game. The reason for this is because Sniper's ultimate is his only activated ability besides shrapnel, which means free and easy ult steals for Rubick. This means to always use shrapnel after using your ult before getting into Rubick's steal range.

Have fun, and happy sniping!