I just started using CakePHP and it's very different from just normal procedural or basic OOP PHP.
I am still learning PHP and still read "beginning PHP/mysql" books that teaches you basic PHP. Also lots of sites online provide code that isn't for a framework.
Is the only way to make non-framework code to say a framework, say cakePHP, by learning cakePHP thoroughly than rewriting the code yourself to fit the MVC model?
CodeIgniter allows you to write things the way you want but really works best when you use it as a MVC platform. You would write all of the PHP code in the controller if you wanted and the application would still work, you could then decide to split out the code for the database into the model and then later decide to put all of the HTML into the view. That's if you would like to do it like that.
I would recommend doing tutorials and trying to use the MVC model as it has saved me a lot of time and is so much better than flat file coding.
CakePHP can be a little restricting as it requires you to follow particular naming conventions.
Hopefully this gives you a good start on a road to learning the ease and speed of MVC.
I think it would be beneficial to learn basic OOP PHP thoroughly before learning CakePHP. I admit Cake is a little restricting about naming conventions but you can customize this to your liking. I would try to rewrite a small PHP application in Cake to get familiar with it. Choosing a MVC framework does save a lot of development time if you take the time to learn on well. For Cakephp the book and API are two very valuable tools. I also suggest using Cakephp 1.3.