Opening a Case
This is usually pretty straight forward on just about any case. Many cases make the process incredibly easy by using latches or buttons that allow a panel to be opened; this would be explained in the instructions for your case. Case selection and different types of cases are explained in these articles.
More traditionally, one removes a few screws and the panel or several sides of the case can then be slid towards the rear and removed. Some cases will have hinges and the panel will swing clear instead of coming off completely. Enthusiast-type cases will often use thumbscrews instead of the Phillips ones so that people who open their case a lot can do it without getting out a screw driver. Note that you can replace the normal screws holding your case’s panels on with thumbscrews (in different colours for under 2 bucks a ten pack at newegg) if you will be working in there often.
These screws are generally along one or more edges of the rear side of the case. They have yellow squares around them in the first picture. Remove them, put them in one of your bowls, and slide the panel off.
Many manufacturers will place bags of screws and other small items inside the case. Since this is also the point at which you can see everything inside the case more clearly than you ever will again, and if there is something wrong you would rather know sooner than later, now is a good time to inspect the case for damage and make sure nothing the manual says should be there is missing. Pull the front panel connectors (the wires coming from the front of the case for things like USB outlets and the power switch and light) out of the way as best you can so you have more room to work.
You can also clear some space in your work area and protect your shiny new case panels by placing them, outside-down, on something soft. Depending on where you are working, a couch, bed, upholstered chair, clean out of the way carpet and so on can all work. This will protect the flanges on their insides and the finish on the outside. Damaging a tab or rail on the side panel can make it impossible to get it back on the case, so it is worth getting these out of the way.