You can do it, I made a career change from Civil Engineering to Developer at 30. It takes some time so don't plan on quitting your call center job soon.

First determine if you enjoy coding and have a knack for it. Some people enjoy it more than others and some people have the ability to quickly track down bugs, solve problems and apply knowledge to solving new problems.

If you're totally new to coding I would recommend starting with the book Head First HTML and CSS. You can find the first version pdf online, order from your library, get it on amazon, barnes and noble usually has it in stock. Work through that book at your computer.

Use google+stack overflow for help. Typically you can google a problem or error and you'll find a proper solutions on stackoverflow.com. This will ring true even as a professional/experienced developer.

Work through the book at a computer working along with it, don't just reed it and expect to learn.

After that create some basic websites of your own, register a domain name. Get an inexpensive shared hosting account. hostgator will work. Learn how to setup your domain, point the a record. Register yourname.com or something you might want to use in the future since you'll have it for a year and might want to renew use for your projects. The hosting account you could cancel after a month or two once you're familiar with setting up domains.

After you're comfortable with that. You could start contacting local businesses and see if you can land some work creating small business websites. It seems there are always small businesses out there that could use a website. In the beginning don't worry about forming an LLC or anything. Write them a simple proposal to create their website for $XXX or $X,XXX. Small businesses don't usually expect to pay a lot for sites and this isn't going to replace your day job but you can make some money and get experience working with clients. Also they will request things like can you make it do this that will expand your skills.

You can charge them for creating the website, for hosting and for maintenance. You can charge a fixed fee for creating the site. Getting started I'd estimate work at 2x your call center rate. Estimate how much time you think it will take, then double that and make that your fixed fee proposal to start. Initially you're probably going to take longer than you expect and might even lose money on projects by taking too much time. But part of doing this work is to learn new things, get more comfortable with your new trade.

I would have them register their domain name since that's something they will always want to keep with their business. A good service is keeping track of their expiration dates (run a who is) and follow up with them to make sure they renew in the future. Especially if they are new to websites/domains.

Charge monthly for hosting and maintenance. I would try charging $50/mo for hosting, maintenance offer a $99 plan that includes once monthly updates to content (up to 1 page). So this could be adding news, updating phone numbers, adding/removing staff, adding a page. You can setup recurring charges through paypal, they can signup with a credit or debit card through their paypal account or you could offer an annual plan that they pay by check.

Ok at this point you'll run in to clients asking can you make my site do xyz. Most likely this will require some server side development or javascript.

At this point I'd recommend getting the book headfirst php and mysql. and work through this book the same way as the first. PHP isn't a super glamorous language but I think it's the best next step.

After you have worked through a portion of that book. Give setting up wordpress a go. wordpress.org. You can install this on a hostgator account the same way. Wordpress is a CMS that powers lots of sites on the web and runs on PHP and MySQL. After you get your feet wet with this you can learn about wordpress themes and plugins. There is alot you can learn here. I think it's good experience. There are lots of WordPress developers out there so I don't think this should be your ultimate goal, but it is another service you can provide to clients to get more experience. Wordpress based websites where they can login and make updates, add pages, or you can set them up in WordPress and make the updates. I find many clients can't even handle making updates in WP and will still end up requesting you do it for them. Always charge them for making updates (unless you have a basic maint. plan that covers it that they pay monthly, get them used to paying for work).

Working with clients don't get overloaded. Always pad your deadlines and try to deliver early or at least on time.

Ok so you're getting familiar with Wordpress and working through the PHP and MySQL book. Once you complete the work with the book start creating some of your own applications. A to do list, something to track something you collect. Then research creating a login and authentication system from scratch in PHP and MySQL. This is a great learning experience.
Once you have completed your own application I would recommend learning a framework. Frameworks handle all the messy behind the scenes stuff you just worked out on your own. But creating it from scratch once will help you understand what the frameworks are doing behind the scenes.

Ok so for frameworks I would recommend Laravel or Rails. This is your ultimate goal as Laravel and Rails developers get paid a good rate.

For Laravel start here (only after completing the books and your own apps)

laracasts.com

use forge.laravel.com for creating servers and deploying your code, learn git (use gitlab or bitbucket or github).

You might also want to start listening to startupsfortherestofus.com start with episode 1, being a developer if your ultimate goal but you should think about having your own products too.

Good luck with the transition.