You can't, because they change constantly in each individuals mind, and even if you could ask everyone sufficiently often (ask every person every second), they would probably not know, because it is not their needs and wants, it is their action (their actual offer or accept of someone elses offer) that matters. Still, you can imagine the valuations and their aggregate. It is a dynamic, organic system. We see only the resulting prices in the market.
If you believed that the USD has lost X% of its value of Y years, how would you be able to prove that assertion?
It follows that you can not prove it. Since it is money we are talking about, it follows that it can not be consumed directly, therefore, what you get for each dollar is what counts. Personally, I like computers, and I can have more computer value now for 1000 dollars than I could in 1913, or more realistically, when I started to grasp the concept of money in the 60's, or, when I started to accumulate value in the 70's. In that regard, the USD has gained value. On the other hand, I could have a professional paint my house for that sum in the 70's, but not now. A consumer price index has to somehow reflect what consumers tend to buy, but what consumers buy is also directed by the offers available. So fundamentally, it is not possible to say. The different consumer price index calculation methods are at best attempts at approximations.
That is also why it is fundamentally impossible to manage the money. Free everything, and let the market decide.