Set up the stepladder so you can position the piece of guttering to attach to the fascia. Make sure that the piece of gutter that you are positioning is at least 2 inches longer than the position it is to be installed; this allows for a 1-inch overlap of gutter with the other pieces. You will need this overlap to seal the gutter with caulking.
Move the ladder to the high end. The gutter should gently slope from one side to the other so that the water will flow toward the downspout. A general rule of thumb is a 1-inch to 1 1/4-inch drop per 10 feet of gutter run.
Make sure the gutter brackets are mounted to the piece of gutter evenly over the length. You should use three to four over a 10-foot piece of gutter. These serve to make sure the gutter doesn't deform under the weight of the water when it's raining.
Take a screw and use a screw gun or screwdriver to attach the gutter to the fascia. You will screw through the gutter from the inside channel directly into the piece of fascia.
Move the ladder down the entire length of gutter and place a screw at several points. A good rule of thumb here is to place a screw at about every 2 feet of gutter.
At each joint with the other pieces of gutter, separate the pieces and run a small bead of silicone caulking to seal the two pieces together.