Most paper doesn't come as squares.  Strangely, we have tons of rectangular paper available, but very rarely will you find a scrap of square paper.  One of the first tricks I learned was how to turn a rectangular piece of paper into a square.  Once you do it a couple of times, you will never forget it.

  First take your paper, and fold a short edge diagonally to meets a long edge.  This should create a two layer triangle attached to a single layer rectangle.

  A triangle is half of a square, so we will be keeping the triangle, and getting rid of the rectangle.  We do this by folding a crease between the triangle and the rectangle.

  Once the crease is visible, unfold the triangle.  Fold the second crease the other direction, and the first direction to weaken the paper at that edge.  This will make tearing it easier.

  Tear the paper at the second crease.  If you find it difficult to rip in a straight line, work the crease more, or moisten it by folding the paper and licking the fold (don't lick a raw edge, you'll get a papercut on your tounge).

  You are left with a square, and a scrap rectangle.  Notice that the square has a fold through the diagonal.  If this is bad for your model, use this paper as a template to make squares without the first fold.

And hold onto that piece of scrap paper.  When you are done with your model, you can try making a smaller one with this piece of scrap.  You shouldn't really run out of paper this way, it'll just get too small to work with.