Whenever you use power tools or machines, you need safety gear. Since you will be creating a lot of sparks with the hacksaw, you should wear a full face shield, long sleeves, and work gloves. It is always a good idea to know what you are going to cut and to what size. As a guide, you can make a full scale drawing with exact dimensions and angles for all parts of the chair frame. That way, when you cut and shred them, you can grab them and hold them against the drawing to make sure they're right.
Set the metal cutting saw at a 45 degree angle to cut the pieces for the rear legs (Image 1). Check the cut piece against the full scale layout making sure it is the correct length and angle (Image 2). Repeat this process, checking each piece for the chair frame against the full-scale design. Long pieces should always be cut first. That way all the short pieces can be taken out of the cut.