Cup measurements: shake or scrape?

I suggest to measure by weight as you'll never go wrong.

Otherwise, I use your second method which is to scoop then use a knifed to rid of excess flour.

Flour is so fluffy and needs to be compacted (somewhat) to get a true cup, therefore measuring by weight always guarantees the same amount of flour.

The real answer is that it depends on the measurement methodology used by the person who wrote the recipe. I have one book that actually calls for measuring by scooping with the measuring cup and scraping it with the side of the bag, which is how the average person tends to measure flour, and results in about 30% more flour by weight per cup.

King Arthur flour (and most other recipe sources) use the "sprinkle the flour into the measuring cup with a spoon and then level with a knife" which most closely simulates measuring sifted flour. This method will generally be appropriate when using professional recipes, unless the cookbook calls for another method. These recipes generally do not want compacted flour. If you are compacting your flour you are almost certain to be using too much.

Many instructional style cookbooks will lay out their measuring methodology at the beginning of the baking section (or the beginning of the book if it is a baking book). But since every methodology and every individual's use of that methodology comes out with a different weight per cup, working by weight really is your best bet.

For bread recipes, measuring by weight is the only way to go. (And yes that means that almost all bread recipes printed need to be converted by guesswork, because you have no 100% certain way to know what the author really experienced.)

"Pro" bread bakers express recipes with formulas using percentages based on the weight of the flour. The flour weight is always 100% implicitly, and then other ingredients are smaller percentages of that (like 0.8% instant yeast, 1.5% salt, 60% water).

Weight is the preferred measurement method for baking as the ratios have to be rather precise and volume is affected by settling, humidity, and storage methods.

Michael Ruhlman's Ratio is a good reference for how the proportions should work.

I was taught to sift then measure, and to scrape the excess off with a knife.

Frankly, I'll measure then sift.

The only exception is Brown Sugar, which is usually lightly compacted.

As others have said, you're essentially screwed if you're using volume to measure flour.

For reference: a cup of flour is between four and five oz (up to a 25% swing, depending on measurement and flour type).

A sifted cup of flour is usually quite close to 4 oz; this is the major reason that you are told to sift flour when baking -- for precision. Of course, weight is also not perfect, since humidity can affect the weight. But, it's FAR more consistent than volume measurements.

I usually trial convert a recipe at something like 4.5 oz per cup and adjust from there.