Depends what you mean by basic piano. To some extent yes. I started off by teaching myself only knowing how to read music from playing violin when I was younger. There comes a time though when you really do need a proper teacher as there is only so much you can learn from a book and you need to avoid incurring bad habits that a trained person would know how to spot.
I got a teacher after 10 months in September 2012 and I enjoy it more now when there is someone to confirm that I'm doing it right and correcting any physical mistakes with hand positioning and fingering. You also progress much quicker with a teacher than if you're teaching yourself.
The John Thompson books are good to start with. I also used "Total Piano Tutor" by Terry Burrows but it's not really a book for absolute beginners and you need to have a basic level of theory.
My teacher told me "There is no such thing" when I asked him for recommendations of a self teaching piano book.
YES - you can teach yourself. But - NO, NOT 'stickers'!
I assume you can drive a car? You don't need 'stickers' to show you which pedal to use, or which gear you are in. Kinesthetic or muscle memory lets you know where you are; similarly with piano or keyboard, provided your Right Hand thumb knows where middle C is, you can work it out from there.
You don't even HAVE to think about the NAME of the note on the keyboard, but if you are reading music the brain/hand should go straight from the note on the line or in the space, to its position on the keyboard. If you have to 'translate' into the name of the note as well, that is another step the brain has to make, which is unnecessary.
I assume you DO mean proper piano ('real' or digital), like Lang Lang; and not keyboard, where the 'automatics' will do the accompaniment for you, while you concentrate on the melody.
I taught myself to play electronic organ, with two manuals and 13 note pedals, with reasonable success, but I already played drums in semi-pro bands, and knew a certain amount about music.
But one thing I DIDN'T realize for a long time - and this is important to make learning and understanding easier - is that middle C in written notation, is on the ledger line BELOW the stave in Treble Clef, and is the same note that is written on one ledger line ABOVE the stave in Bass Clef.
For years I struggled, thinking Treble and Bass Clef were two different entities, when in fact each is a continuation of the other. This is known as the Grand Stave (or Staff) and is HERE .
Another thing that is very useful to 'get you head round' if you can manage it is: Why is there no Black note between E & F, nor between B & C? (I will leave you to work/find out the reason; PM me if you can't.)
Yes, the John Thompson books are good and I used them for a while. Also good for adults are all the Kenneth Baker piano books, and he also has series for organ and keyboard.
When I was trying to improve my Bass Clef playing, I tried some simple Mozart pieces, working out the Right and Left hands separately. I was surprised to discover that there was just as much good melody in the Left Hand part as in the Right, and it wasn't just an accompaniment.
When I was a primary school TA, I taught recorder, and a bit of keyboard. Children always had difficulty remembering Chords. If one understands where Chords 'come from' it makes it easier to work out or remember them; in due course if you need to know that I'll tell you a bit about it.
If, however, you already know most of this stuff, I apologise for going into so much detail.
Get a teacher, please, please, get a teacher - you will save yourself money in the long run. Bad habits are difficult to undo, and you will inevitably develop some. It just isn't as simple as putting finger 1 on key A etc...
However, if you must go it alone, I would recommend Piano Adventures for Adults www.musicroom.com/se/id_no/0335082/details.html - comprehensive, and explains everything, and comes with CD backing tracks to play along. Lots of short pieces that only introduce one new concept at a time and plenty of practice at each stage. Piano Time is fine for adult returners to piano, but it tends to move too quickly for most people, and you don't get very much repetition of ideas. Piano Adventures is a more gentle, manageable progression.
You can teach yourself to read music and you can teach yourself theory from a book but nothing can take the place of a living breathing piano teacher who can teach you correct technique. There is a bit more to learning and playing the piano than just hitting the right notes from sheet music.