Here's a short tutorial based on my experiences with training my own ear and the methods that I've used over the years...
If you don't take anything away from this tutorial, please at least take this: you can't train your ears if you can't hear! Basically what I'm trying to say is that the most important thing to think about when thinking about your ears, is that you want to keep them healthy! If you can do this, training your ear will become second nature if you're taking the right steps. I don't claim to be a doctor or know much about the details behind the human ear, but I do know that this day and age it's very easy to start losing your hearing at an earlier age and quicker rate than previous generations. We live in a world where there is loud noise around is all the time and the equipment that we have has the capability to get louder than ever before...
The bottom line when it comes to your ears is that you need to be wearing proper hearing protection when you are in a loud environment; trust me when I say you'll be glad that you did. If you feel that the cheap ear plugs you can buy in the store are uncomfortable or don't allow you to adequately hear, I'd highly recommend getting yourself a pair of custom made ear plugs. If you want to hear some more thoughts on this matter, please consult my other tutorial, "Health Tips For Keeping Your Ears Healthy."
Moving aside from keeping your ears fresh and healthy, let's talk about some ways to actually develop your ear. The first way that I started to train my ear before I even played an instrument was by simply listening to a lot of different music, and a lot of different music all the time. I still do this and still feel that it is one of the best ways you can get accustomed to your ears and can get them going. Having the knowledge of a lot of different genres of music is really essential for being an engineer. While many engineers will record only a specific genre of music, if you're serious about becoming an engineer you'll undoubtedly need to know about a plethora of different types of music.
Beyond having an eclectic taste and knowing the different platforms of music out there, simple practice is really the best way to train your ear. The most that you work and try new things, the more you will find solutions that work for you in the recording studio. Learning how to manipulate signal processors, mic placements, and effects all depend on what your ears will tell you, so it is obviously important to be in tune with them. The more that you work on projects, the more you are able to recognize the features of a sound and based on past experiences will be able to react accordingly. There's definitely no better way to ear train than by simply practicing your craft.
While you may not see overnight progress, I guarantee that the most you work in the recording studio and listen to music, the more comfortable you will be with your ears and with your instincts. If you can practice your craft a bit every day, you'll be giving your ear new experiences on a daily basis and this, I have found in my own experiences is the key to training your ear.
I hope that those new to the game found this to be helpful!