This post is copied from the Koha Mailing list. It is the fabulous Ian Wall's response to a question someone had about what is involved in hosting one's own Koha server...
To host your own server, you'll need some level of comfort with Linux command line operations. I recommend a Debian Squeeze server. You can either purchase a new physical machine, or create a virtual server on an existing machine or in the cloud. You can quickly fire up a server in the cloud using services like Amazon Web Computing, Rackspace or Linode. This saves you from having to install an operating system on a piece of physical or virtual hardware.
Once you've got the server up and running, you'll need to install Koha. You can do so from the packages, from the git repository or from the downloadable tarballs. Personally, I recommend the git installation, but my understanding is that the packages are a little more user-friendly at the installation phase. Are you going to be developing on Koha at all? If so, then a git installation is definitely the way to go, so you can track your local changes, and format them in a way to submit back to Koha!
In addition to installing Koha itself, you'll need to install it's dependencies. That includes MySQL (with which you said you were familiar), Zebra and Apache (Perl is almost always installed by default). The installation instructions for Koha will walk you through those steps. Further, if you want your Koha install to be able to send email notices, you'll want to install and configure an MTA (Message Transfer Agent). I recommend Postfix, but exim4 also works. The default SendMail also works, but I've found it a bit less flexible and thus a little more frustrating.
You'll also need to be comfortable with the crontab, so you can set up nightly jobs like fines, overdue notices, and backups. This is one part syntax (knowing how to put an entry on crontab) and one part text editor familiarity (vi or nano, typically).
If all this seems a bit overwhelming, you're not alone. If you need assistance, I'm sure there are Koha support companies in your geographic region who would be happy to assist you with installation, and may even provide hosting options. Check http://koha-community.org/support/paid-support/ for a listing of known support companies from all over the world.