Hold on to your hat: the average adult human actually loses something closer to 500 million skin cells per day¹! Don’t worry, though. Your body is made up of far more cells than that: about 30 trillion, or nearly 100,000 times more than the number of skin cells lost each day. (As an aside, your body contains even more bacterial cells – about 39 trillion².)

You may have heard that the dust that shows up in your house mostly consists of dead skin cells. The short answer to your question is that scientists usually just collect the dust that people shed₃ and weigh it! Sometimes they do this by having the subjects of the study wear special pajamas for a while and then collecting the dust from the inside of the pajamas. But it turns out that the most accurate way to collect shedded skin cells is to have people wear a small cup over a patch of their skin for a day. The skin cells fall into the cup, after which they can be collected and weighed.

If you know the average mass of a dry skin cell, the area of the opening of the cup, and the area of skin on the person’s body, you can then calculate how many skin cells the person lost over the course of the day!

Sources:
1. Milstone, Leonard M. “Epidermal Desquamation.” Journal of Dermatological Science 36, no. 3 (December 1, 2004): 131–40. link.

2. Sender, Ron, Shai Fuchs, and Ron Milo. “Revised Estimates for the Number of Human and Bacteria Cells in the Body.” PLoS Biology 14, no. 8 (August 19, 2016). link.

3. Roberts, D., and R. Marks. “The Determination of Regional and Age Variations in the Rate of Desquamation: A Comparison of Four Techniques.” Journal of Investigative Dermatology 74, no. 1 (January 1, 1980): 13–16. link.

I'll first point out that the number of cells lost per time is not at all consistent in internet sources. Although the number of cells lost always seems to be 30,000 - 40,000, the amount of time required to lose these is given as per minute, per hour, or per day. Regardless, the reported rate is not from a direct counting of the number of cells lost by a person; it is certainly an estimate from various known quantities. One way to estimate the rate uses the number of cells comprising an average person's skin and the life cycle of a skin cell. The current "best estimate" for the number of cells in the human body is 37 trillion. One can then use that number to guess the number of skin cells by assuming that 1/7 of the cells are skin cells just as skin is ~1/7 the total weight of a person. The life cycle of a skin cell seems to be better quantified, with turnover of all skin cells typically being listed as taking about a month (~30-40 days). Multiplying all of this out:

37*10¹² total cells/person * 1/7 skin cells/total cells / (30 days * 24 hr/day * 60 min/hr) = ~2 million skin cells lost per hour, or ~34,000 cells lost per minute.

The per minute rate calculated here is consistent with SOME values found, but clearly not all. The lack of details on the calculation of those other values complicates the comparison. Further, the estimates for the number of cells vary widely (could be up or down by 10x) and can dramatically affect the final result. But, if new and more accurate numbers come out, this is one way that the rate could be calculated.

The skin is made up of three layers, the epidermis, dermis, and subcutaneous tissue. The skin cell shedding occurs in the epidermis. The shedding of skin cells is also known as desquamation. Scientists has many ways to measure desquamation. A vacuum-powered apparatus can be used to collect the shedded cells in a given area of skin. A passive collect cup can be also glued on the skin of a test subject. Once the number of cells shedded in a given area between a given time is measured, we can extrapolate it for the total number of cell a person shedded each day. You might find the attached article interesting:
Roberts D, Marks R. The determination of regional and age variations in the rate of desquamation: a comparison of four techniques. J Invest Dermatol. 1980 Jan;74(1):13-6. doi: 10.1111/1523-1747.ep12514568. PMID: 6985944.

Here's an idea about the research - if scientists study the lifetime of skin cells in a lab animal, maybe with a radioactive tracer molecule, to get these results, then they can calculate the numbers you found: "Humans shed and re-grow outer skin cells about every 27 days - almost 1,000 new skins in a lifetime." Check out the link - it has lots of fun facts: here.