listen to recordings, as many different artists as you can find. Listen enough so that the entire piece is in your head, in various interpretations so you don't automatically go to "copy" one of them. Listen while sitting quietly. Try to envision what the score might look like from listening alone. Listen while reading the score, see how right or wrong your vision of the score was. Start to break the score apart finding unique and repeated phrases and content. Start doing a harmonic analysis of the piece. Perhaps find the major melodic and harmonic ideas and re-writing the score as an outline. Notice how you've done a LOT of work before you've even touched the piano? The point being - study the piece from every conceivable angle before you touch the piano. Then begin doing some investigative work by sight-reading the piece hands together. Find what will be easy, and what will require technique that you do not yet have. Break everything down into chunks that are manageable (read all of Bernhard's posts on this site for lots of good stuff) and start at it. As Bernhard would say (paraphrased) "piano is not complicated, it is complex" - that is, a piece is huge collection of easy tasks. Take the most virtuosic piece you can imagine, and then take only the first two notes of that piece - those two notes are likely very easy.
So the point being, don't just dive right in and try to read through before doing any preliminary work. The more work you do away from the piano first, the less time you will actually have to spend at the piano once you begin. (of course if you are advanced enough that you can sight read through anything right away hands together, this probably doesn't apply)
Topic: starting new songs