You can get Fake Books at music stores or by ordering them online. You can also get a version of the same concept when you come across a simple notation of a song. A Fake Book, or the like, has only two things to guide you. First, you will get a melody line in the treble clef. This will usually only show one note at a time - no chords - and it will be a simplified version of the song.
The second thing you will get with this simple music is a letter above the staff. The letter signifies the chord you are to play in the bass clef and possible add to the treble clef if you are skilled enough. There will be a letter above the staff each time the chord changes.
By learning the chords, you are preparing yourself nicely to be able to use a Fake Book with ease. You can use the straight chords or invert them. You can play them as running chords where you play each note separately in succession. You can come up with any rhythm you choose for the bass clef.
Using a Fake Book is a somewhat creative endeavor. You have to use what you know to fill in the blanks that are left by incomplete score. In that regard you are in charge of inventing the music. You can find Fake Books that are fairly current, with music you have heard recently on the radio.
Yet, if you want to really come up with your own original song or instrumental piece, you can do it better by learning to improvise. You can learn very complex theory about improvisation, but you can begin with the information you already have. You need to know mainly about scales and chords.
Choose a scale to work from; a C scale may be the easiest for you since it is all on the white keys. Next, choose some chords within that scale. For the C major scale, common chords to use are F major and G major. This is because they do not have any sharps or flats in them.
Make up a chord progression. It can be C-F-G-C. Practice playing these chords with your left hand. The base chords are usually played below middle C, but that is not a rule, by any means. Play them wherever you see fit. Play them as simple triads or invert them. Play them in any sequence. Play until they come naturally.
When you are comfortable with your chord progression, you can begin to improvise a melody. Just play with your right hand, one note at a time to make a melody line. It may not seem like music at first, but if you keep trying you will eventually come up with an interesting melody line.
You can also improvise on a melody you know. Say you want to play Jingle Bells, but you do not have the music. You can quickly pick out the melody. Then, you can choose chords to go with the melody based on the key, or scale, the melody is in. If you do not have sheet music, these are ways to play without it.