How to know what the letters mean in math formulas?

A mathematical text would define the notation it uses, either within the body of the text or in an index of symbols at the start or end of the text, unless the notation is really common. For example, a high school text would not define the symbol for ordinary addition or subtraction.

If you are ready to see what the notation in your example means, read on. Otherwise, stop here.

In your example $F=\frac{dp}{dt}=\frac{d(mv)}{dt}$, $t$ is time, $m$ is mass, $v$ is velocity, $p=mv$ is momentum, and $\frac{d}{dt}$ is not a fraction but the derivative function. You will learn about taking derivatives in a calculus course.

You take classes, and hopefully the people teaching those classes explain what the symbols they're using mean. Alternately, you read textbooks, and hopefully the people writing those textbooks explain what the symbols they're using mean. In this particular case, taking a physics class and a calculus class (alternatively, reading a physics textbook and a calculus textbook) would tell you what all of the relevant symbols mean.

(In particular, in this case $d$ is not (quite) a function and the bar does not (quite) denote division. This is not something you can just figure out.)

I don't understand how you're supposed to know what symbols mean without asking anyone. Do you expect that you can learn what Chinese characters mean without asking anyone (not even a dictionary)? Did you learn what English characters meant without asking anyone?