Installing and running SSH is pretty straightforward. As soon as you install the openssh-server package SSH will be running on your server. In order to access the server over the Internet, you will have to make sure that port 23 is open on your browser. Once you have the port open, you can access your server from your internal network by using the command:
ssh username@hostname
or from a remote location, with the command
ssh username@ipaddress
Accessing ssh remotely means you will have to know your home IP address. Since most home users do not have a static IP address you can circumvent having to look it up by using a service such as dyn-dns or no-ip. Both of these services are free, and have Linux clients whose sole purpose is to map a dynamic URL to a static IP.
Every server needs security. For the home server, it is a good idea to close down any unused ports, and limit access by minimizing the number of users who have sudo (super user) access. You should also install and run anti virus software such as ClamAV. Read the Tobias Rice article on the subject for detailed instructions on how to install and set it up correctly.
Finally, you should disable the X-server in order to save CPU usage and prevent wandering hands from making changes. In Ubuntu the command is:
/etc/init.d/gdm stop
Read the free book Securing and Optimizing Linux for an indepth discussion on Linux security.
A home server running Linux is fairly inexpensive and easy to set up. Having one creates a centralized location to place the family's photos, music and videos. The added bonus is now you can back up that one server regularly, and everyone's data will be preserved.
If you are interested in setting up a server for your small business, there is much more to be considered. Take a look at Tolga BALCI's series of articles for more information.