A Schengen visa has from: and to: dates and duration 90 days.
A person has such a visa, which totals to 102 days, from: until to: dates.
I seem to have read that from: and to: limit the entry of the person, not the visa. The duration is still 90 days. So entering on the day of to: still gives you 90 days. Which means you need a stamp in the passport, to prove you have not overstayed.
Is this how it works or have I missunderstood?
For a Schengen visa, for any day of your visit, you need to respect all of:
So if you have:
Then:
So:
Some other countries allow you to enter at any time during the validity of the visa, and then stay for the max duration (so example #5 above would be OK). This is not the case for Schengen visas.
So no, if you enter on the last day of validity of the visa, you cannot stay, you must leave the same day.
I seem to have read that from: and to: limit the entry of the person, not the visa. The duration is still 90 days.
This is the central incorrect point in the question. In fact, the FROM: and TO: dates limit your presence in the Schengen area, not only your entry.
(There is another important point that is missing from the other answers, which is that the DURATION will never be greater than 90. If the number is 89 or less then you may stay in the Schengen area no more than the given number of days in the Schengen area. If the number is 90 then you are only limited by the 90/180 rule. This is only relevant if the period delineated by the FROM and TO dates, inclusive, is longer than 180 days, so it does not apply to the visa contemplated in the question, but I mention it because we do occasionally see questions about such visas on this site.)
Is this how it works or have I misunderstood?
No, this is not how this works, the visa must also be valid during the whole duration of the stay. If you want to stay beyond the “to:” date, you need another visa (it's possible to combine two visas as long as you do not exceed 90 days in any 180-day period).
There’s a good explanation here
Schengen Visa sticker validity The labels «FROM», «DU» and «VOM» are followed by the first day you are permitted to enter the Schengen Area, and the labels «UNTIL», «AU», and «BIS», stipulate the date by which you must leave the Schengen Area.
Duration of stay label The label «DURATION OF STAY» «DUREE DE SEJOUR» and «DAUER DES AUFENTHALTS» and the one immediately next to it with the words «DAYS», «JOURS» and «TAGE» tell you the number of days you can remain in the Schengen Zone on each visit while your visa is valid.
Entering on the day of ‘to’ would mean you have to leave the same day.
For clarity, as mentioned in a comment by @phoog, the DURATION OF STAY number does not apply to each visit but to the life of the visa. For example, a multiple-entry visa with a duration of 20 days allows a single visit for 20 days or multiple visits totalling 20 days; it does not permit the bearer to be in the Schengen area for 40 days if they enter twice.
