The easiest way to listen in on AnimeLemming Radio is by visiting the ALR Live365 homepage, and clicking on the "Play" button found in the upper-left area of the page (with the big yellow button and the speaker on it)

It'll look something like this little doodad to the left of this column...you click it, and it'll open a small web browser window which will, alas, show you some spammy advertisements. Once that's done, it'll ask you how you want to listen, be it through the LivePlayer, or through your MP3 Player. Pick your choice, and you're on your way!