If you're running your own web site, the chances are that it will be on a Unix or Linux machine, although sometimes your web host will be using Windows software.
Most autoresponder software currently available for use on your web host is designed to run using CGI (or Perl) scripts. Some programs are now starting to use PHP instead.
If you're not sure what programs you can run on your web host, you should be able to find out the details either from their regular sales page or from your technical support contract.
Running CGI or PHP programs on your web host is fairly easy, but you will need some degree of technical knowledge. If you need help uploading your regular pages, don't even think about hosting a program on your web site unless it offers an installation service.
Because autoresponders need to run on a regular basis, you will need a way to make sure that your messages are sent out. The higher end programs listed below will require you to have CRON enabled on your web site host. This is a program that acts in the same way as Scheduled Tasks do on your regular PC: it runs programs at regular intervals specified by you. Your host may or may not allow you to run CRON tasks - generally speaking, cheaper hosting packages don't allow this option. Lower end programs make use of something called a 'fake CRON'. This usually works by placing a fake image link on a high traffic web page. When the link is 'viewed', it calls a program to check to see whether or not the autoresponder has sent out your messages today and - if not - it makes sure they are sent out.
The most common web based program is called AutoResponder Unlimited. It is readily available all across the internet, sometimes as part of a software package. The cheapest place to buy it is usually on Ebay.
If you've got a low budget and aren't anticipating running a big list, then AutoResponder Unlimited could be the program for you. One warning though, in my experience the program can occasionally lose entries from your mailing list for no apparent reason. So make sure that you set the program such that it emails you every time a new subscriber joins your list and also that you backup your list regularly.