It is really simple.
1. Open a browser (chrome, firefox, ie, etc) and go to the osrs login screen.
2. Download the mirror mode zip file, extract it and move the jar file to OSBot\Data folder.
3*. Start the OSBot client and select mirror mode. Log into the client if you haven't already. Click "Add Bot" and wait for it to mirror the browser.
4. Start a script and watch the same thing happen in the browser and the client.
* If you notice that it doesn't load the osrs login screen, then it is most likely that the browser and the OSBot client are running different versions of Java. Once is probably using 32 bit, while the other is using 64 bit. Make them use the same version of Java and everything should work.