You can record any sound produced by your sound card using Sound Recorder
coming with Windows. In my Windows XP SP2 I can launch it by
1. Clicking Start->Standard->Multimedia->Sound recorder;
2. Running sndrec32.exe from a command line or "Run..." dialog.

Using this program and a PC with attached Mic you may get a .WAV file.

You may also suggest your visitors to use Audacity sound editor or
any Direct sound recording program.

A user can also use a portable player with a Mic to record sound. It is usually very easy to get mp3 or wav file and to transfer it to the computer.

Once you have mp3, wav, etc. file on your computer, you can upload mp3, wav or any other supported file to a web-site. Any web-developer knows how to use the upload button in the HTML form.

For non computer savvy users and for the majority of others you should provide step-by-step instructions on using your service. These instructions should be easily available from all the appropriate pages.

As for technical help, you may outsource your project using Freelance project marketplace. Some of them are free for buyers, so you can sign up for free and post your project for free. After that you may communicate with IT professionals using the project forum.

I suggest you to describe your project as good as you can and post it on as many free services as you can (there are only 3 large service I can suggest - see the link above). Doing this you will be able to get lots of responses that might get you new insights.

Selecting an IT pro is not an easy task, but rating and experience can tell you a lot. Also Safe escrow payment allows you to minimize risks.