Go to the App Store and download The Unarchiver. It's a free download.
The app will prompt you to open it after it finishes downloading. A screen will appear where you can select the types of files you want The Unarchiver to open for you. The most common types are already selected.
Click on the Extraction tab and select how you want the app to handle the folder that's created when you open a RAR file.
Your RAR file should display The Unarchiver icon. If it doesn't, right click on the file, choose Open With, and select The Unarchiver.
Double click on your .rar file.
The Unarchiver will open a file window where you can choose the destination folder for your RAR extraction folder. You also have the option to create a new folder.
Once you have selected your folder destination, click the Extract button at the bottom right of the window.
Your RAR file is now a folder, and you should be able to access all of the files that were compressed into the RAR.