Android - How can I install an app given only its APK file?
Use DropBox. Put the APK in your DropBox folder. Open up the DropBox app on your phone, find the apk, tap on it, and it should download it to your phone and then install it.
Use the SD card. Plug your phone into the computer via USB. Mount the SD card drive. Copy the APK into the SD card. Unmount your phone. Browse to the APK using a file browser app such as Astro. Tap on the APK and it should present to install it.
There are countless other ways to do this, but these two are probably the easiest.
Another way...
Place the .apk file onto your SD card (by using your phone as a mounted drive).
Enable applications from unknown sources (go to Settings > Applications > then verify that Unknown Sources is selected).
Use an application such as Installer or APK Manager to install the application.
I prefer using the ADB. However, It's a little less user friendly. This isn't the easiest way, but it will work without an SD card and will work without the device being internet connected(some devices(tablets) aren't).
At the command line you would type:
adb install "full-absolute-path-to-apk-here.apk"
The "tools" directory of the SDK must be in your path for the adb command to work.