WordPress really needs to do something about the confusion between their .com service and the self-hosted .org.

It sounds like you've got a .com account (your web address would look something like
http://www.yoursitename.wordpress.com). Plug-ins are only available if you have your own domain name with hosting through a hosting service like Bluehost, HostGator, GoDaddy, etc.
I always explain to people that wordpress.com sites are sort of a 'preview' of what the self-hosted version are like, but with limited capabilities.
It gives you a taste of what can be done through the widgets, but with the self hosted version there are tons of plug-ins that give you even more capabilities. Including contact forms that can be created to do things like the reservation form you want to create.