Ultimately, ML is a mathematical discipline. You can ask for a gentle approach that gets you to the foot of the mountain, but "if you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." If you want to be more than an amateur, there's not much substitute for getting comfortable with math at the level of, say, Kevin Murphy's book.
The good news is that the required math is fairly elementary - calculus, linear algebra, probability and statistics, all freshmen or maybe sophomore-level topics - so it shouldn't be beyond reach of a motivated developer able to set aside some time to learn. MOOCs and organizing study groups with friends/co-workers can help a lot here as well.
If no, what are the great resources for starters?
The videos / slides / assignments from here:
http://ai.berkeley.edu/home.html
This class:
https://www.coursera.org/learn/machine-learning
This class:
https://www.udacity.com/course/intro-to-machine-learning--ud...
This book:
https://www.amazon.com/Artificial-Intelligence-Modern-Approa...
This book:
https://www.amazon.com/Hands-Machine-Learning-Scikit-Learn-T...
This book:
https://www.amazon.com/Introduction-Machine-Learning-Python-...
These books:
http://greenteapress.com/thinkstats/thinkstats.pdf
http://www.greenteapress.com/thinkbayes/thinkbayes.pdf
This book:
https://www.amazon.com/Machine-Learning-Hackers-Studies-Algo...
This book:
https://www.amazon.com/Thoughtful-Machine-Learning-Test-Driv...
These subreddits:
http://artificial.reddit.com
http://machinelearning.reddit.com
http://semanticweb.reddit.com
These journals:
http://www.jmlr.org
http://www.jair.org
This site:
http://arxiv.org/corr/home/
Any tips before I get this journey going?
Depending on your maths background, you may need to refresh some math skills, or learn some new ones. The basic maths you need includes calculus (including multi-variable calc / partial derivatives), probability / statistics, and linear algebra. For a much deeper discussion of this topic, see this recent HN thread:
https://news.ycombinator.com/item?id=15116379
Luckily there are tons of free resources available online for learning various maths topics. Khan Academy isn't a bad place to start if you need that. There are also tons of good videos on Youtube from Gilbert Strang, Professor Leonard, 3blue1brown, etc.
Also, check out Kaggle.com. Doing Kaggle contests can be a good way to get your feet wet.
And the various Wikipedia pages on AI/ML topics can be pretty useful as well.