This is fairly self-explanatory, but here are some tips:

When you first start, pause your game, then navigate to the Options sub-menu and turn "Disable Vita-Chamber" ON;
Save, save save. About to go into a new room? Save; Hear some enemies running about? Save; Haven't saved in the last 5 minutes? Save;
Do your homework. Once you obtain the Research Camera, start snapping shots like a Hipster at the dinner table - it'll make your life a lot easier;
Hack everything. Hack Vending Machines to lower prices, and hack Security Bots for some handy companions;
Use Special Ammo. Use Antipersonnel rounds for Splicers, and Armor-piercing rounds for Big Daddies and machines;
Hey, big spender. You can only hold a maximum of $500, so don't be afraid to spend your money.