Summarize this article in one sentence.
Use your old brake lines as guides, cutting each line ahead of time so that you can visualize how much extra tubing you have (or need to buy, if you're short). "Chamfering" is simply creating a slope at the end. You want to use a file or a bench grinder to slant roughly 1/2" of the end. It will look a bit like a pencil without the lead in the center. You want to install the fitting so that it can be screwed on over your flare. Make sure you add the fitting now, as it can be difficult to add later. Most lines are flared on both ends, so make sure you add two fittings, pointing opposite directions, before beginning. The long free piece of the flaring tool should be clamped firmly into a table vice, keeping it in place as you put pressure down to flair the line. The actual flaring tool should hang over the edge of the table, as the brake lines need to drop down below the tool as you work. You can do this free-handed if you don't have a vice, but it is much easier with one. This is the part you'll be flaring, but you don't need much exposed to make your connection. 1-2mm above the flaring base should be enough. Note how, in the video, the tube is in the far left hole of the flaring tool. Thus, the left-most screw is tightened first, keeping the tube in place, before the screw on the right is tightened. These only need to be hand-tightened. You want a nice flat surface to create your connection. Make sure it has a nice flat top. Take a small reaming tool and insert it straight into the top of the line, rotating it with even pressure down into the tube. This will ream out the inside edge of the tube.

Summary:
Cut the tubing to the required length with your tubing cutter. Chamfer the ends of the tubes that you'll be double-flaring. Slide the fitting onto the line, with the threading facing the side you just cut. Mount your flaring base in a vice. Slide the tube into the appropriate sized hole on the flaring base so that the chamfered end barely pokes out the top. Tighten the flaring base around the tube, starting with the screws closest to your brake tube. File down the top of the tube so that it is flush with the flaring tool. Use a reaming tool to clean out the inside edge.