SubscribeAs far as starting a podcast, I guess I would start by asking what you already know about podcasts so I would know where to start in my explanation. Having the studio would put you well ahead of the pack for the most part. Once you have a recording, publishing it as a podcast is easy. You have to decide where on the internet to host it (more later), handle licensing questions if you're playing music (more later on this too), and do something so people know it exists (item three below).
First, where to host it. You already have a web site, so you have some idea what this is like, but be careful. Podcasts tend to be large files (40 megabytes per episode is not even beginning to stretch it), and so the more popular your show, the higher the bandwidth costs will be for you. On the other hand, you can host it with someone like Podshow (where mine is) or Podango (which has a revenue sharing scheme, nice). These sites provide free hosting and pay all the bandwidth costs. In exchange, you're driving traffic to the site, and they make money from advertising on the site. When you finish an episode, you post it to their site and add some show notes, they do the rest automatically.
Second, music licensing. If you want to play most commercial music, you're talking to ASCAP/BMI and the bill is not small. On the other hand, there are may sites (check wikipedia's "podsafe" entry for links) that provide podsafe music. This is music that is licensed under different terms from ASCAP/BMI. It may be a Creative Commons license, or something like Podshow's license, but it usually comes down to "you can play the music without paying a fee, we consider it a fair trade for the exposure, but you're obligated to tell your listeners where to buy our music." There are other licenses in between which charge fees that scale down much further than the ASCAP/BMI setup. None of it is hard, but it's something important to pay attention to.
Third, letting people know you exist. The first thing I would recommend is adding your podcast to some of the common places people look for podcasts: iTunes, Podcast Alley, Podcast Pickle are the three biggies. It's easy to do, and gets you at least to where people can find you if they know to look. The second step is to create a short promo and make it available, then contact some people with podcasts who might have an audience overlap with you. So far, the general attitude favors helping each other over rivalry.
That's a quick start. If you want more let me know, but for now I don't know what areas to cover in more detail or where I might be boring you.