Use a tool such as the WPV XAP Deployer or the official Windows Phone 8.1 SDK to push the file from your PC to your phone via USB.
If your phone supports it, you can also copy the XAP file to your SD card, open the Store app, select "Install local apps," and choose Opera Mini from the list. Troubleshooting Common Issues opera mini for windows phone 8 download
Opera Mini for Windows Phone 8 & 8.1: A Complete Download and Usage Guide Use a tool such as the WPV XAP