If you're using a website client that already has an "Upload Mp3s" feature built in, click on "Choose File". (Myspace and Facebook both have this feature). A directory with your music will pop up. Click on the mp3s' that you'd like to upload. The directory window will go away and the mp3 will be ready to upload. Click on "Upload" and then repeat the process with any other mp3's you'd like to upload.
If you're using a client that requires a separate host for your mp3's, consider free sites designed for this purpose. Upload your files there, following the website instructions for uploading your files there.
Once the mp3s are uploaded to a host site, you'll be able to create a link on your website and for instant listening. Create a link inside your website client and then hyperlink it by clicking on the "hyperlink" button (looks like a small chain linked together). A box will pop up asking you to put in the web address of your mp3 host site. Type in the address of your site into the box and this will link the two pages together.