I registered the domain address on GoDaddy.com: $12.
I registered the Blogspot address thesongbirdproject.blogspot.com: Free.
I registered the Gmail address firstname.lastname@example.org: Free.
I designed the header myself on pixlr.com: Free.
I painted the bird logo myself: Free.
I take pictures using iPhone's Instagram app: Free.
I record videos and post them to YouTube: Free.
I post links to photos from Picassa (Google's Flickr-like service): Free.
With permission, I use photos from Flickr's Creative Commons: Free.
To post songs, I've used a service called OpenDrive: Free.
To back up Word documents of lyrics, I use Dropbox: Free.
The blog is supported by Google and Amazon adds that can earn me money: Free Money.
Really, the main cost is the time and effort it takes to post.
When it comes to songwriting, this means there are ways to find inspiration without letting it hurt your wallet. I was flipping through Wired Magazine a few months ago and came across an interesting photo by Caleb Charland. The first thing I did was Google his name, click "images" and all of the sudden I had hundreds of his photos there in front of me. And what did it cost me? Nothing. Also, the public library is an incredible resource for free books and movies (as long as you remember to return them on time). It's also common to work out trades with other creative friends for recording time, press photos, design work, etc.
Recently, Dr. Jeff Cornwall (head of Belmont University's Entrepreneurship major) featured The Songbird Project on his blog. Read it here.
Keep writing (and bootstrapping),
P.S. - I literally bought these $200 boots from Goodwill for $3.99. How's that for literal bootstrapping?