For me, the most difficult aspect of cutting paper is cutting a straight line. Depending on the thickness of the paper, the paper can buckle under your knife. Or, the paper buckles as you cut towards you. So I have developed some tricks that I use when cutting paper.
Rule #1: When cutting straight lines, use a piercing tool for the starting and ending points of your cuts. The problem with cutting a line is that you many times you end up cutting past the point of stopping. When doing this, you end up with hash marks at the end of each cut. By using pin holes, you know exactly when and where to start and top.
Rule #2: When you can, cut one line in one direction and then cut the connecting line in the opposite direction. In the illustration above, for line one, I would cut north to south and then I would cut line six, east to west. Most people would cut line one--north to south--and then cut line six--west to east. The problem is that the paper is weakened and cutting line six this way could tear the paper when exerting pressure.
Rule #3: Cut parallel lines before cutting perpendicular lines. I have numbered the lines above as I would cut them. I would make all north to south cuts first before making east to west cuts.
Rule #4: Use your ruler to apply pressure on the paper. In the illustration above, most people would start with line # 5 (because they are right handed) and then continue to cut line #4, #3, etc. The problem with this is that the paper is weakened because you have cut it. When you go to cut line #4, the paper has pressure applied to it and will likely curl or buckle and eventually tear. To alleviate this problem, cut line #1 above first. Then place your rule on line #1 to cut line #2. The pressure of the ruler should prevent any buckling or curling of the paper as you cut line #2. Move your ruler to line #2 to cut line #3, etc. When you are cutting lines 6 - 10, I rotate the paper 90 degrees so that I could be cutting the lines from north to south (rather than east to west). I find it easier to cut in the north-south plane but some people prefer to cut west-east plane.
Rule #5: The pressure applied should be on the ruler and not on your cutting tool. When cutting with a ruler, keep the hand pressure on the ruler so that it doesn't move. Putting the pressure on the cutting tool will tire your hand but also allows for the ruler to slip and ruin your cutting. Please keep in mind, it is much better to make several passes with your cutting tool (which is easier to do when you are using a ruler) than to make a single deep cut.
Rule #6: Find out what ruler works best for you. I have a variety of rulers that I use and will have a separate post on that topic. Usually, I use a cork backed 12" ruler for most of my work.