How to find IP address of a machine on network?

[Chris G]

I have just installed ubuntu onto a machine and have connected it to
my LAN.  The router provides DHCP and the new machine is up and
running on the network.

How do I connect *to* the machine?  I need to know its IP address and,
as there are a few devices which get their address by DHCP it's not at
all obvious what the machine's address is.

Eventually I will probably give it a fixed address (for this reason
among others).

-- 
Chris Green