'I have in my hand a piece of paper....'
«Tengo en la mano, un trozo de papel....»
'Piece' me parece un poco difícil, pedazo/trozo/pieza ¿cuál es la diferencia?
y aquí podríamos tener tambien 'hoja'...
...'lonja' supongo sólo tiene que ver con el jamón etc. ...'slice'
y podría ser «Hay en mi mano...»?
[The above is a bit academic, I thought it was a famous sound-bite from Neville Chamberlain, prime minister when the war started
'I have in my hand, a piece of paper, signed by Adolf Hitler...'
but Wikipedia has:
He is showing the piece of paper to a crowd at Heston Aerodrome on 30 September 1938. He said:
"...the settlement of the Czechoslovakian problem, which has now been achieved is, in my view, only the prelude to a larger settlement in which all Europe may find peace. This morning I had another talk with the German Chancellor, Herr Hitler, and here is the paper which bears his name upon it as well as mine (waves paper to the crowd - receiving loud cheers and "Hear Hears").
Not so catchy.]
'Piece' me parece un poco difícil, pedazo/trozo/pieza ¿cuál es la diferencia'
In this case they mean the same, more or less: take a rectangular piece of paper, tear it, and any of the smaller pieces (fragments( that you get are "trozos/pedazos de papel". "Pieza de papel" is a much less common term, and it is more used for parts in a machine, a game, a musical composition, etc.
For piece of paper I'd just say "una hoja de papel", or simply "un papel".