i'm really new to the linux os and i was having the same problem with with no-ip on ubuntu server 12.4
after a bit of digging i found a solution.
you need to install the gcc and g++ compilers, This will also install GNU make.
sudo apt-get update
sudo apt-get upgrade
sudo apt-get install build-essential
to install No-IP Linux Dynamic Update Client Ubuntu 12.04
tar xf noip-duc-linux.tar.gz
sudo make install
you should get asked for your email add and password
just enter them and bobs your teapot
this worked for me and i'm up and running;)