Assuming you already have a "zip" utility installed (like Winzip or IZArc), simply extract (or unzip) the contents. How the person zipped the aircraft up will determine if some of this is necessary or not. Normally you'll have the aircraft itself with all it's subdirectories, possibly a gauge folder, an effects folder and maybe a documentation folder.
Move the actual aircraft folder to the SimObjects/Airplanes folder. Inside the effects folder, select everything there and move it to the effects folder. If there are textures included, those must be moved separately into the Texture folder inside the main effects folder. For the gauges, look inside the gauges folder that was zipped with the airplane, normally you can simply select all and move those files to the main gauges folder. If you see anything inside that looks like another zip file (called a "cab" file) do not try to unzip those, they need to stay zipped and moved to the gauges folder as is.
Usually that's all there is to it. If you don't have a zip utility yet I would suggest IZArc (freeware) because if you ever get to this point, it will also allow you to produce "cab" files which I don't think you can with Winzip.
One other side note about gauges. There may be instances where the gauges are found inside the panel folder. It's probably best to leave them there unless the readme has instructions to the contrary. By all means, if there is a readme file with the zip file, "read it". There may be special instructions included for that particular aircraft that require a slightly different method of installation, so while the main instructions I listed above will work for 98% of all addons, you should still check the readme beforehand to be sure.
