Over the years I have had many, many students. The fact that you have some musical knowledge is a great start. At some point you will more than likely need the help of a profession teacher as their is a lot more to music than just playing notes on a written page. You can begin by printing off some of the beginner music that is currently on 8 notes, then move up to "easy", "intermediate" and etc.
Learn to play "all" the major scales and get them under your hands. Not just one octave, but be able to play 4 octaves with both hands at the same time. Learn their chords and their progressions. I know that sounds boring but the sooner you the get keys under you fingers the faster you will progress!!
"USE A METRONOME" and count out load! If you don't you will start playing songs that sound good to you, not what is written. You can listen to many of the songs that are available on 8notes by listening to the midi file that is associated with it. There is also a metronome on 8notes.
There is nothing more horrible than practicing a mistake.
Now comes the hard part, "practice". Set aside a time each day where you can be totally free of interruptions and begin practicing. Each day start with your scales and chords for 5 - 10 minutes. Learn one scale at a time and get it to the point where you can play 4 octaves, both hands together, with the correct fingering, with your eyes closed. Set you metronome slow and play 4 notes/beat, then gradually increase the speed.
Work on no more than 2 -3 songs at a time. As you master one, more onto another. The amount of time you practice will determine your success. A minimum of 45 minutes/day is a good place to start. At some point you will also need to start memorizing them as well. Another great tool for learning is to record yourself, then listen to it. DO NOT use any pedals. they should only be used sparingly, and at a much later date.
When I was younger I would practice 3 hours/day. Even though I had a full time job and a family, I would get up a 0500 and practice for 1 1/2 hrs, then another 1 1/2 in the evening.
Finally, I recommend that you learn on an acoustic piano as opposed to a digital piano, the feel of an acoustic instrument is totally different than a digital instrument.