One of the best ways to become effective with Cakephp (or any framework or language for that matter) is to actually create a project you care about with it. The Cakephp documentation has become fairly good, so simply by using it as a guide it’s certainly possible to create pretty much any type of project.
I wouldn’t recommend working on a project merely for the purpose of excercise, or something without any real world value.
Learning something like Cakephp takes a lot of time and effort, it will at times be extremely frustrating and that’s why it’s important to work on a project that will be worth it in the end, at least in some way that matters to you.
So instead of trying to “study” it, i think it’s much better to just use it as a means to an end.
But that being said - while doing so, it’s also important to keep the principles and best practices that Cakephp proposes in mind, such as “don’t repeat yourself” and “convention before configuration”. There’s the “cake way” to do almost everything, which is the ideal way to do something within the context of Cakephp. It’s worth putting time and effort into finding these ways, instead of simply hacking stuff together, because even though it may be more work in the short term, it will certainly benefit you more in the long run.