The easiest way of connecting to BrumSpace chat, is via the web client, at chat.brumspace.org.

However, you may prefer to connect using a regular Internet Relay Chat (IRC) client.

Take a look here for a comprehensive list of clients.

Once you have a client, simply connect to the irc.freenode.net server, and join the channel ##brum

For more information about IRC in general, take a look at irchelp.org.