How can a band create a mailing list to send out show responses
I'm actually not an expert on maillists, but there are specialized apps designed just for this purpose. Some mail servers have built in support of maillists. For example, I use Xmail on my Linux web server. Xmail has a maillist feature, although I've not used it yet.
As paradox814 suggested, you can "roll your own" using a database or even a simple text file. Whether to use a database or a text file depends on 2 factors really.
How many people do you expect to have on your list? If less than 5,000 or so, a text file should work fine.
Do you already have access to a database? If not, figuring out how to get one setup and how to work with it can be daunting to a newbie to say the least. So if you don't already have a database, then a text file looks attractive.
If you will have 10's of thousands of subscribers or you know how to work with a database, the database is a better way to go.
So being able to manage the data is one thing. Another important part of many maillists is the ability to subscribe or remove yourself. You probably want that, too. So whether you end up using a db or a text file, you'd want to develop a web page front end that allows people to add or remove themselves from the maillist.
Sending a mass mail is then just a case of writing a program to loop through the addresses sending your email to each one. This gives you an overview of your options. Once you decide to code something, I'm sure you'll have plenty more questions!