openHAB comes as a platform independent zip file, which you only need to extract to some folder (please note that the folder must not contain any spaces).
You will find the following folders:
conf: This contains all your user specific configuration files.runtime: This contains the openHAB binaries, there should normally be no need to touch anything in here.userdata: Here you will find all the data that is generated during runtime: log files, database files, etc. In theory this should be the only folder where openHAB needs write permission on.addons: Here you can drop all add-ons that you want to use with openHAB. This can be addons from openHAB 1.x and 2.x likewise. All compatible add-ons can be found in the addons zip file, which is available as a separate download.
Many add-ons require some configuration. In openHAB 1.x, this was done in the central openhab.cfg file. In openHAB 2.x this has changed to separate files in the folder conf/services, e.g. the add-on 'acme' is configured in the file conf/services/acme.cfg.
Likewise, the syntax in the configuration files has changed to not require the namespace anymore, i.e. instead of
acme:host=192.168.0.2
in openhab.cfg you would now simply enter
host=192.168.0.2
in the acme.cfg file.
All openHAB 2 add-ons are made available as a separate download, which also contains all compatible 1.x add-ons for convenience.
Once you have configured your runtime, you can simply start openHAB by calling start.sh resp. start.bat on Windows. Point your browser to http://<hostname>:8080 and off you go!