Summarize:

Use the tape measure running down the edge of the tile cutter to line up the tile where you need to make the cut. Vinyl cutters can typically be rented from hardware stores so you don't have to buy one for a single job. Call your local store to see if this is an option for you. Twist the screws on either side of the top of the cutter to raise or lower the blade so that the tile will fit neatly under it. The blade doesn't need to touch the tile at this point, as moving the handle will lower the blade. Firmly move the handle from the upright position down toward the base of the cutter. You can do this step quickly or slowly, just make sure to press the handle all the way to the lowered position so that the blade cuts through the entire tile. Move both pieces of cut tile away from the cutter. Raise the handle if you have another piece to cut, then repeat the process.
Place your tile in the vinyl cutter. Adjust the depth of the blade by turning the screws. Press the handle down. Remove the tile from the cutter.