On PC Battlelog is mandatory to play BF4 for Single player or multiplayer. You will need to click on multiplayer, then server browser, and then adjsut your server browser filters to see the maps and game modes that you wish to play. After you adjust the filter settings save and refresh and then find a server that you wish to play on and click on the play button (square with triangle in it) and you will join the server.
If you are having problems with clicking on buttons in battlelog and they do not respond be sure to disable any flash blockers, script blockers, and popup blockers in your browser and that should help.
