When used with nouns, the distinction is actually deceptively simple. With saber, we refer to concrete data about something. In essence, we refer to the attributes of some thing. Let's say we want to talk about a book:
- Sé el título (del libro)
- Sé el lugar de publicación (del libro)
- Sé la editorial (del libro)
- Sé el tema (del libro)
- Sé el color (del libro)
All of these attributes fit nicely in questions in the format ¿Cuál es el/la ______ del libro?. But in this same context, we can't say sé el libro. The book isn't an attribute of something else1.
When we want to refer to the thing itself, rather than the individual facts/data about it, we use conocer which instead of fitting a question like ¿Cuál es el/la ______ de ______? instead answers ¿Cómo es _____? This then expresses knowledge of all the attributes of the thing simultaneously.
For an example of how this plays out in some of the cases where their usage seems to overlap:
¿Sabes el precio de las manzanas?
Here, the thing in question are the apples, and we want to know if you know a literal fact about them — their price. The answer would be a single datum, like $2/kg.
¿Conoces el precio de las manzanas?
Here we want to know if you know cómo es el precio. While that could indeed include the current price, it also includes things like its normal variation, whether that price is higher or lower than normal.
¿Sabes (el nombre de) la capital de Canadá?
Topic: Canada. Just give me the answer. Sí, sé (el nombre de) la capital. Notice the possibility for an implied el nombre de, though its not strictly required.
¿Conoces la capital de Canadá?
Topic: Ottawa. Are you familiar with the city of Ottawa?
This is why with people you almost always use conocer (besides its to meet meaning) with people — people are inevitably asking if you know the person and their corresponding attributes. Rarely is the person himself an attribute of something else, but it's not impossible and then we switch to saber: ¿Sabes el presidente de Guatemala? Es el Gen. Pérez Molino.
1. Note that I refer to this context. The book maybe indeed be an attribute of something else in a different context, for example, the first book published by an author (in which case it becomes an attribute of the author).