To start using OBS Remote the first thing you need to do is install the plugin. The installer can be downloaded here.
The latest version of the plugin currently requires at least version 0.50b of OBS. The installer will locate your installation of OBS, provided you have installed it using the OBS installer. If you have a test build you may have to manually download the plugin dll and directory.
After running the installer, if you launch OBS, you should be able to see OBS Remote in the OBS plugin window.
By default OBS Remote has password authentication enabled, default password: "admin" (no quotes). The password can be reset through the plugin configure dialog, from OBS (plugins > OBS Remote > Configure).
Password authentication was added in lieu of ip-address based filtering (i.e. the dreaded .hosts file) in plugin version 1.1.
After installing the plugin all you have to do is launch the client. You can either navigate to client.obsremote.com. Or click the big green link at the top of these pages. The first time you start the client you will have to specify the hostname for the computer running OBS that you want to connect to. For the same computer you can either enter 127.0.0.1 or localhost. For another computer on your network you can enter it's hostname or ip-address (how to find ip-address).
After successfully connecting to OBS, the client will remember the hostname and will try to automatically connect to it in the future. You can click the connection status icon in the lower left to open and close the connection dialog.
After the client is connected you can start/stop streaming, switch scenes, turn sources on and off, control the volume, and monitor your stream statistics.
Once the client is connected, you can also setup the stream preview options. For now, this feature only works if you are streaming on Twitch.tv. First, click on the gear icon in the upper left next to the scenes list. This should bring up the dialog seen to the right. From here you can enter your twitch user name, and specify if you want to preview your stream and/or your chat. You can also configure the stream preview to only appear when you are actually streaming (I suggest this by default.)
Currently your stream has to be embeddable for this to work. Right now the stream preview implementation is kind of kludgy, I hope to have this working better with the Twitch API soon.