The frist thing I would look into is using a database backend instead of your CSV file. From what you describe, a simple flat file will quickly become a liability when it comes to searching and updating the data. Don't know if you are familiar with SQL already - if not, I'd check out open source solutions such as MySQL or PostgreSQL. These are all well supported in Perl, using (by now rather old-fashioned) Perl DBI or the more moden DBIx::Class (or others).
The old-fashioned way of making a dynamic web site was Perl CGI but I would not recommend doing this anymore. Use one of the modern web frame works. Personally, I am using Catalyst and I have used CGI::Application in the past. Both are good. Catalyst comes with a steeper learning curve, so CGI::Application might be the faster way to get you off the ground.
The thing about modern frameworks, is that they follow a so-called "Model-View-Controller" design and it is worth learning a bit about the concept first. In brief: the model contains all the "business logic" of the web app - in your case that would be what you have in your existing scripts. The Controller is the bit of the app that takes user input, then asks the model to do something with it and finally asks the View to render something - usually a html web page.
Using such a framework means that your existing back-end (the scripts you have written) basically stay as they are and you just write some additional code to interact with it and present the results.
The only thing you might have to do to your existng code - if you haven't already done this - is to make them proper modules that can then be "use"'ed in your web app with a clear interface to keep the Model code nicely separated from the rest of the web app.