Whether you are wanting to become a professional photographer or just want to better your own personal photos, here are a few of my opinions on the processes you need to go through. I've been there and am still learning more and more about these things on a regular basis!
First, and foremost, begin to learn your camera and how to use it manually! While your new fancy equipment can do great things on auto, you have so many more options to make your photos AMAZING when you figure out how it works. This also means you need to figure out how the camera actually functions which can be a confusing and time extensive process. For a general starter lesson on camera settings check this out http://www.slrphotographyguide.com/camera/settings/.
Purchase books, read articles online, ask a friend that knows what they are doing, and practice, practice, practice! You will have a hard time remembering all this information overload if you don't use the advice you've been given. Books designed for you camera will help you work the camera, and will generally provide you with additional information on what each functions does, but to fully understand all the functions cameras collectively, you may need to research further on how all of the aspects of lighting affect the final image your camera produces. For example, you might read that the aperature is this certain number on your camera and lowering the number by turning a certain dial lets more light in, but that doesn't really tell you much about how to apply that along with ISO or what to use in certain situaions. If you are shooting in Manual, you need to know this information because changing aperature affects ISO and you need to know how! That's why you need to fully understand the terminology and apply it as well, not just how to change it on the camera.
The second step in figuring out your camera and it's functions is to decide on a starting place. No photographer ever has just gone out after reading a book and figured it all out in the beginning. I started with learning aperature and began playing with that "A" setting exclusively. Once you feel as if you've mastered one setting add something else to mix and gradually work your way up to shooting in straight up Manual. This takes time and practice...don't be discouraged! Check out some starting point advice here http://digital-photography-school.com/aperture-and-shutter-priority-modes/.
You also need to learn the basics of constructing eye-pleasing photographs. Books and online articles can help you here as well and this is much easier than leaning the camera. But remember....photography is subjective and if you like it, then all is well! Check out this link for more info http://lifehacker.com/5814174/basics-of-photography-composition-and-technique.
This is must when learning your new camera and with your introductions to photography...just have fun with it and don't stress yourself out with it so much that our get burnout! You will see the quality of your images increase as you get more experience and advance in your skills. I was frustrated at first too because I wanted to know it all "NOW"! It takes time and patience, but has a big pay off in the end if you stick to it!
Once you've reached a certain level of satisfaction in your work, get more equipment and learn about the lenses and flashes (if you have a DSLR). This takes time as well, unfortunately, but the better understanding you have of lighting and your cameras functions, the easier this will be!
Finally, get a photo editing program and figure it out as well either by just playing around with it or buying a manual to read and study. This will help you enhance your photos digitally, especially if you are still learning and they aren't as "perfect" as you would like for them to be. I have Corel Paintshop Pro and it is good for the beginner as it is very simple and user friendly. Photoshop will most likely be too complicated for the beginner and can be REALLY expensive!
Hope this helps! Feel free to add or comment below. Happy Photographing!