Step 1: Download the version of macOS or OS X that you want to use. 
Step 2: Open Disk Utility and insert your USB drive. 
Step 3: Click the View dropdown at the top right of the window, and choose Show All Devices. 
Step 4: Find your USB drive in the list and select the highest parent. (This is usually the name of the device’s manufacturer.) Select it. 
Step 5: Click Erase at the top and give it a name - this can be the name of the OS you’re installing, such as Yosemite. Choose Mac OS Journaled (Extended) and click Erase. This may take some time. 
Step 6: Open Terminal - this can be found in the Utilites folder of your Applications folder. Then, type ‘cd ’ (with a space) but don’t press enter. Open a Finder window and navigate to the folder that your installation .app is located. Click View in the menu bar, and enable ‘Show Path Bar’. You’ll now see a bar at the bottom of your Finder window showing where you are in your computer’s file system. Right-click (or click with two fingers on a trackpad, or control-click else) on the name of the folder that your installation app is in, and click Copy Path. Go back to Terminal and press Command and V to paste the path - then press enter. Terminal should now say ‘machine:your-folder username’ where machine is your Mac’s name, your-folder is the folder that your OS X or macOS installer is located, and username is your account username. To ensure you’re in the correct directory/folder, type ‘ls’ and press enter. You should see your .app installer listed. If not, try this step again.
Step 7: Copy and paste this code into Terminal and press enter. Ensure you get the correct command for the version you’re installing. For Mavericks 10.9 to El Capitan 10.11, paste in ‘sudo /mac-installer.app/Contents/Resources/createinstallmedia --volume /Volumes/your-usb --applicationpath /mac-installer.app’. Change ‘mac-installer.app’ to the name of your installer app - e.g. ‘Mavericks.app’. You should also make sure that you change ‘your-usb’ to the name you gave your USB earlier. For Sierra 10.12 and later, paste in ‘sudo /mac-installer.app/Contents/Resources/createinstallmedia --volume /Volumes/your-usb’ where ‘your-usb’ is the name you gave your USB earlier. Once you’ve entered the correct command, press enter and type in your password. Press Y, then enter, to confirm that you want to erase your USB drive. Terminal will now write the operating system and its installer to your USB drive. This will take a long time, depending on the size of the OS and the speed of your source file’s location and the speed of your USB drive. 
Step 8: Once you’re done, unplug the USB and shutdown your Mac. If you’re installing to a different Mac to the one you made the USB on, you need to shut down the destination Mac. 
Step 9: Insert the USB to your destination Mac. Power it on whilst holding Option ⌥. Then, select the USB drive using the arrow keys and press enter to boot. The USB will typically say ‘Install OS X’ or ‘Install ESD’. It will also have a different icon to the internal drive, and is probably the only device other than your internal storage. 
Step 10: Use the macOS / OS X installer to install the OS. You may have to use Disk Utility to erase the internal drive first.