A powersupply will contain many connectors. Lets discuss this step by step.
1. Unplug power from system.
2. Disconnect all previous connections from old powersupply.
3. Unscrew powersupply from case and remove the unit.
4. Insert new power supply, and secure with screws.
5. Plug in your 20/24 pin connector to motherboard.
6. Plug in 4 pin AUX power connector (usually near processor).
7. Plug in devices such as Hard Drives and CD/DVD rom drives. (Most are Molex (4 pin) or SATA (Flat) connectors)
8. Plug in Video Card Connections (If Applicable). This is usually the 6 pin PCI-E or Molex Connections.
9. Seal up PC and plug in powersupply.
10. Turn on and test!