Make sure you have a working Go environment. See the install instructions.
First we need to get the required dependencies. beehive itself is part of that list so the main executable can depend on our sub-packages:
go get github.com/fluffle/goirc/client
go get github.com/hoisie/web
go get github.com/muesli/beehive
Now we can build beehive:
git clone git://github.com/muesli/beehive.git
cd beehive
go build
API docs can be found here.