NEVER leave the power cord plugged in when you have the case opened! Especially in newer computers! The highly touted fast startup by Windows 8 systems comes from the fact that the computer goes into a modified sleep state rather than fully powering down. This not only allows many processes to keep running but obviously it means the entire system is fully powered. If you want to curl your hair and your computer, leave it plugged in. On the back side of most computers there is a real power switch. The On/Off switch on the front doesn't power down most computers!
Get a static bracelet from an electronics supplier if you plan on touching the internals of your computer. That's a bracelet that has a wire that can be fastened to a grounded metal object or inserted into the grounding port of an electrical receptacle. Just for cleaning you don't need a grounding bracelet unless you're very shaky.
There are special anti-static vacuums you can buy for cleaning electronics. These have well grounded hoses. Regular vacuum cleaner hoses are not wire cored any more and of those that are, the wire is not grounded to the vacuum case. A sharp spark of static and your electronics are toast. Don't use your household vacuum, even to blow if you can use the exhaust port.
Canned air is best. If you have an air compressor, as was mentioned elsewhere, you can force some moisture into your computer unless the air first passes through a desiccant - dryer cartridge, or you allow the computer to air dry under an air current (fan) for at least an hour before you put the case back on and hook up the power. Using canned air is like spray painting, keep the nozzle or the tube at least 8" away from any object. If there's a propellant used, it cools when it expands and can thermal shock your electronics. Pure compressed air has no propellants to worry about, but still, to be safe from damaging the surfaces, keep the nozzle or tube at least 8" away. Use a suitable paint brush, artists type to loosen stubborn dirt and Also mentioned was blocking the fans from spinning. YES! Spinning the fans too fast can ruin the bushings and cause the little fans to seize and stop running. Use a small wooden dowel rod to reach into the fan blades to hold them still.
I noticed that you said you don't know how to open the case. Puzzles they iz! On some you can remove a few screws on the back and the case will easily slide back or up. On others you remove the screws and lift the case about 1/8" and then slide it back. On others you slide it back 1/8" and then lift. On others there are actual latches you have to find and release. A few you have to spread one edge of the case to disengage some tabs. Do a web search on your brand and model with the term 'To remove the case from __' or see if you can find a full service manual to download from the manufacturers' site.
Next, how often to clean? I've got two dogs and four cats in a house with forced air heat. About every three to five months is plenty for me. For other homes, you might go 2 months or even a year or more between cleanings. The answer for you? Take a look at the vents and just inside through the vents with a flashlight every few months and you'll get your answer.
Finally, if you feel the least bit uncomfortable doing this, find a family member or a friend who isn't, or take your computer to a good, well recommended shop for them to do it. For some people this is nothing, for others, it can be a top level challenge.