Tell me if this goes above your head.
First, you need to install this (or a similar) wordpress plugin if you want to stream from your wordpress blogs (as in your readers don't have to leave the page).
http://wordpress.org/extend/plugins/audio-player/
Second, I'm guessing you have your own webhost (not just domain name)? If so, you can create a folder with a title of your own choice in your Public folder, then upload your audio files by ftp (filezilla is a good free app) to that folder, and then follow the instructions here (
http://wpaudioplayer.com/usage/) for streaming your audio files on your pages. If you choose this, make sure the streaming doesn't go above your bandwidth limit.
If you want to use a separate host, check this link (
http://www.audiohostings.com/) for free hosts, copy the link from your host, and use the same instructions here (
http://wpaudioplayer.com/usage/).
Or you can just use a separate music host that gives you a widget to use on your blog.
http://zshare.net/
http://www.toofiles.com/en/audios-upload.html (I tested this and it provides a widget you to insert into your site.)
There are a lot of audio hosts out there that you can upload your files in addition to these two, so look around, but make sure it either has a link directly to the mp3, or a widget to put on your own site. If it gives you a direct link to the audio file, you can then use it with the wordpress plugin. Or you can use the widget code on your site.
PS- Someone else can probably give a simpler solution. Oh and the main reason you'll want to use a wordpress plugin it'll probably look better with your site and you won't have to deal with ads, your files being deleted, and your files being
easily downloaded. If you don't have a webhost to store your files, you can always use a free one (maybe...).
http://www.000webhost.com/ is good.
PS 2- You can also use dropbox with the wordpress plugin. Just tested it and it provides a direct link.