With WordPress blogs you can embed audio players directly into the blog posts, as shown below.
It is best if you upload your audio to another site and just link to it in your blog. One good place to upload and store your audio is the Internet Archive. They will store your audio files for free, you can add Creative Commons licensing to them (or not), and you can find lots of other audio there that you can use (check the licensing provisions for each item first).
Audacity is not really a web-based tool, but it is a free and open source audio editor that you can download and install on your computer. I use it all the time and highly recommend it. Learn much more here.
Odeo.com is a totally free audio and podcast website where you can create podcasts, upload audio and make them available through iTunes or with embedded audioo players (or both). A full blog post about Odeo is available here.
This is what an embedded Odeo player can look like:
One workshop that I have given several times is titled “Podcasting without Fruit.” Follow the link to see the presentation materials using a Google Notebook. The reason it is called without fruit is because the workshop is designed for Windows users – you don’t need an Apple computer or Apple software to create podcasts!!