My science advisor often comes to me late or not at all.

Firstly, I run Civilisation using D-Fend Reloaded as a front
for DOSBox on a 64-bit Windows 7. (I was too young when MS-
DOS was actually used to use it, and I do not know how to use
DOSBox on its own, either.) This glitch has not always happened;
I have played Civilisation for months.

Oddly, though, yesterday and to-day, if I try to play Civilisation
something odd happens. I have tried to play thrice, always as the
Germans. Twice, my science advisor never appeared at all to let
me select a technology; another time, he only shewed himself three
turns after the game started. I do not know what is causing this or
how to fix this; how may I get the game to function again? Re-starting
my computer does not help.

Most probably just change Tax rate (Game/Tax Rate or '+' on numeric keypad) to, say, 30% Tax, 70% Science after founding a city. Quite often, the first city just get 1 trade (the "arrows" in city screen) after founding, which translates to 1 gold/0 science with the default 50%/50% setting. This occurs e.g. when there is no river square nearby.

Later, build roads (and railroads) and establish trade routes with caravans to maximize trade.

edit: I am probably underestimating your knowledge, apologies. Just trying to sort the most probable things out.

I think "Renergy" have answered this question.

First of all remember that you can only accumulate "light bulbs" (science) after you build your first city.
After that, you need to put you city's workforce working on a square that has trade value (grassland, ocean, river...).
Sometimes, the city square itself has trade value (it depends on the terrain where you built your city).
If trade arrows are too few, depending on your tax rate (which you can adjust), sometimes no "light bulbs" are produced, only money ("gold coins") and so the science advisor will not show.

Please note that during the first turns sometimes the science advisor comes up late even if the "light bulbs" are already piling.

But that's no problem because once he appears and you select the technology you wish to develop, any "light bulbs" already stored are used.

Check it out!

How to use Dos Box:
Double click
Type this
mount c c:\<name of your directory it's held in>
C:
civ

Alt Enter to make full screen