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A lot of times you can avoid the need to actually sideload APKs through a USB connection or the SD card. First go into your SETTINGS > APPLICATIONS then check the box to allow UNKNOWN SOURCES to enable installation of apps that aren't from Google Play. The steps may vary a little depending on your version of Android. Many times developers will include a QR code link along with the link to the APK, so you can be in your laptop, click the link for the QR code, and use Google Goggles (or other QR code reader of your choice) to scan the QR code right off of your laptop screen. Then it will directly download to your devices and install without the need to go through all of the other steps, assuming the developer included the QR code link. Obviously this poses some risks, so be cautious.
The website MakeUseOf answers that very question with a longish article containing some helpful graphics. Bottom line: You need the APK file of the app you want to install, which MakeUseOf calls "the hardest part of the entire process." Once you get the APK file, you can transfer it from your computer to your Android device using a USB connection. Then follow the MakeUseOf instructions for installing.