If you have FrontPage and your web host supports FrontPage Extensions then you can set up a form in FrontPage which will write its returns to a text file. Yopu can also tell it to email you the form submission as well, so every time someone hits the submit button you will get an email containing the results of the forms fields and a copy of the results will be written to a text file on the web server. This is one of the real strengths of FrontPage.
The advantages are obviously that you don't need a web host to support ASP and Access databases (FrontPage can create them for you too though, if you want it to) and you also don't need MySQL or PHP. It all depends on the FrontPage Extension support from your web host and whether or not you have FrontPage available to use.
There are lots of alternatives though.
You can set up an email message rule to filter any mail that is sent from your web form into a specific folder in your email client Inbox. From there you can set up various ways of exporting the form field results into Excel or Access to play with.
If you have FrontPage I'd look to using it for your forms and have it store in a text file as well as email you. That way you can download a copy of the text file on a regular basis and append its results to your database with a simple import since it is a comma delimited data text file which any database program can deal with.
As fourm member suggests you could go for Access as a database on the web server and use ASP pages to populate it with information from your forms but unless you already have these options they involve Windows IIS hosting and can become costly. PHP and MySQL are another combination that work well and most web hosts support them, however, you need to know how to implement them and while we can help you do that the FrontPage solution is possibly your easiest by far.
Can you tell us what your web host supports and which web authoring software you have available ?