There's a few options available, however if the term sideloading is one that baffles you then fear not as there's a much easier way to get around things and that's to install the Amazon Appstore.
BlackBerry and Amazon recently announced a partnership that will see the Amazon Appstore as a native BlackBerry 10 app in the future when BlackBerry 10.3 hits the scene. Until then you can just follow these simple instructions to install Amazon and get your fix of apps that are available for Android devices.
Step 1: Download and install the Amazon Appstore
Go to the Amazon Appstore download page in your BlackBerry browser (www.amazon.com/getappstore). Tap the "Download the Amazon Appstore" button. The Downloads window should pop up asking you where you want to save it and what the filename should be; just tap Save in the top-right, then tap the file when it's done downloading. If the download window isn't there, tap the overflow menu button in the bottom-right (three little dots), and tap Downloads.
The Appstore should start installing after a short "Processing" indicator. Tap the Install button in the top right, and tap Accept on the pop-up window which informs you of the device permissions that are required for the app to run.
Step 2: Run and log in to the Amazon Appstore
Find the Amazon Appstore icon on one of your home screens and tap it, or simply tap the magnifying glass icon from the home screen at the bottom in the middle and type "Appstore" in the search box at the top. Tap the Appstore icon in the search results.
Enter your Amazon e-mail and password, and tap the "Sign in with my Amazon account" button. If you don't have an Amazon account, tap the "Create account" button and follow the steps.
Step 3: Download and install Android apps
From the Appstore home screen, you can swipe up and down to view featured and recommended apps, tap the magnifying glass in the top-right to search for something specific, or tap the menu button in the top left (three dots) to browse categories.
When you tap on an app you want, tap the button in the top right of the entry listing the price of the app. If it's a paid app, you'll need to tap the button again to confirm the purchase before the download begins.
And that's a wrap
Enjoy. You'll have to bear in mind that until we see BlackBerry 10.3 things are not totally official so you may well find some apps that don't work. There are plenty that do though so have fun trying them out.