Once you download your basket, you'll get a .zip file. Inside that zip file will be all of the content. You need to first extract the contents out of the zip file - which is as simple as drag and drop. You can just drop the files onto your desktop for a temporary place.
Then, if the content you downloaded is sims3pack format, all you need to do is double click and open it. The Launcher will open and will install the content for you. You can do whatever you want with the sims3pack file - some people like to tuck them away somewhere in case they ever need to install their content again, other people simply delete them.
If you end up with .package files, they are slightly more difficult to install. There are instructions for those listed here.
Note that you need to know which format your CC is in. The .sims3pack method does NOT work for .package files, and the method for .package files does NOT work for .sims3pack files. Sims3pack files will show the game icon. Package files will usually just show a blank icon. Also, if you hover over the file, it should tell you what format it is.