Welcome to the marvellous World of Piano!

Your learning rate will depend a lot on whether you have learned any kind of instrument before or not. If you are new to all kind of instrument playing, you will first encounter a fairly steep learning curve where you have to understand a whole new concept. If you are not - then you know already what it is like.
Just don't buy the romantic BS about "natural talents", "progidies" and similar. The only talent you will need is the ability to be stubborn, diligent and have stamina. Well, you also need to be humble enough to take instructions, but I suppose I didn't need to write that, really ...
Playing the piano is more difficult than most people think before they have tried themselves. Learning the first basic chords and where to find the keys is rather simple, so is learning the simpliest pieces and learning how to read music ... but fully mastering piano playing is a lifetime's work. After your first lovely honeymoon with the piano you face the harsh reality where you work and work and nothing seems to happen anymore, and here is where most students quit, with the excuse that they were not talented enough. Those who are much better than you seem to learn everything in no time with minor effort, while you bang your head in the wall (or on the keyboard) over and over again, and still you think you sound like a cruel parody on Lack of Talent. But don't worry - it is perfectly normal, everybody struggle from time to time. Learning is a fascinating and often uneven process, sometimes the brain need a lot of time for processing a new ability. When nothing seems to happen on the surface, it often means some major changes are taking place deep within. Be patient and don't lose faith in yourself.
That is one of the reasons I love piano playing, by the way. It is such a beautiful study in the science of learning and mastering new skills.
You have to enjoy the learning process itself, not just your end goals (like being able to play this and that). The road to these goals involves more steps than you can imagine in beforehand, but that's why you have to see them as STEPS, all of them necessary, not obstructions. Enjoy the ride!
When I picked up piano playing again after nearly three decades of "poor maintenance", I happened to do something that was rather good: I assigned myself 20 minutes of daily practice time in the beginning. Not less, NOT MORE. This helped me getting into the routine without having to turn my everyday life upside down. So, if you don't know how to fit practicing time into you present daily schedule, I suggest you start with just a few minutes a day. And yes, you will find them. Throw your television set out if you have to ... Stop when your time is up, even if you really want to proceed. Then you will be eager to start next session. And when it is a natural part of your everyday life, you don't need further instructions about this.
And YES, keep on listening to the music, go to concerts, learn everything there is to know about pianists, music styles, composers, piano brands ... everything. Go for it, all in. You will not regret it.
Here is something that makes MY blood boil, for sure ... Heard this piece live just a few weeks ago and I'm still up in the clouds. Too difficult for me, still, but some day ... some day ...