Yes, having an .apk file, you copy it to your phone and open it from there, the "Package Manager" opens and asks you to install the program.
When this is done, your application will be installed.
In addition, it is not possible to download .apk files from the Android Market. Since .apk is a simple zip archive and contains the entire structure of the application (also .class, which makes it vulnerable to decompilation). You can find some APK files via ethernet, but they are distributed there from the developer and not from the market.
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