It is very easy to get a twist during the forging of a blade, all it requires is not holding the blade, or the hammer, at a uniform angle as you forge over the whole length of the sword. Double-edged swords give you double the chance to make this mistake. Twists also show up in the heat treating, but this is less common than forging them in.
Swords heat treated in the Japanese manner (hard edge, soft back) are remarkably easy to straighten compared to fully quenched (hard all the way through) blades – the trade off is they are also remarkably easy to bend.
Bending forks (which look like this:╒ ) are used to take out twists by placing the blade in a vise at the start of the twist, and applying torque with the blade between the prongs of the fork.
Twists are controlled by careful forging, careful heat treatment, and careful remedial untwisting during the finishing process, but hopefully if you do a good job on the first two, you don’t need the third.
