You'll need two things, or three.
1. Screws, yes. get the right size, thread pitch, and length to fit the holes in your drive. Hardware store maybe, although they often don't have ones this short. Computer shop ought to have plenty, but be sure they're the right size ans thread pitch.
2. SATA data cable - ribbon form usually with 7 wires. Any computer parts shop has these if you did not orer one - not likely to be coming with the bare drive. You do NOT need a separate power supply connector - should be one already on the end of wires coming out of the PSU. If not, you have two choices of adapter types to get from a computer parts shop - either one that adapts an empty 4-pin Molex (for older hard drives) to a SATA power connector, or one that converts one SATA connector to two.
3. You MUST do two operations on the new unit after installing in your machine before you can use it. These are Partitioning and Formatting. The tools you need are all there in Windows Disk Management as sturm has indicated, although he gave no details. Alternatively to make it easy on you, go to the website of your HDD's manufacturer and look there for a small utility you can download for free to do these jobs for you. Sometimes they are called Disk Initialization tools. Sometimes they are part of a larger set of utilities.