When you are properly grounded, have removed component cards and hard drive from the system, and disconnected the power supply, it's now time to remove the current motherboard. Be very careful and take your time at removing the screws and make sure that you have indeed removed all of them before trying to remove the motherboard. The screws are very small, so make sure when you've removed on, you place it in a baggie or container.
When all screws have been removed, carefully and gently remove the motherboard from the computer case. If you have an anti-static bag (usually if you retained the box), place it in there; otherwise place it carefully in your area (make sure to clear space around it). Now it's time to place the new board in. Make sure you have read the instruction manual before hand, as it will usually describe how to place the motherboard within the case and what some of the onboard stuff is and does.
Place the new motherboard within the case, making sure you are grounded (either physically touching the case or with a wrist strap); line up the holes on the board with the screw markers. Make sure it's lined up correctly and then begin to place the motherboard screws. It may be a good idea to just place all screws within the motherboard and then screw them in.
Once you've gotten the motherboard in, make sure that it's secure and unable to move. You will be able to reinstall the components.
Here's a video tutorial for a visual.
Image credit: MSI motherboard @ Tiger Direct.com