Learn Spanish (Latin America): El abuelo lee el libro.

For basic declarative sentences like this one, yes! The structure is Subject (El abuelo) + Verb (lee) + Object (el libro). Spanish word order can sometimes be more flexible than English, but this SVO order is the perfect standard to rely on right now.

How would I make this sentence negative to say 'The grandfather does not read the book'?

You simply put no directly in front of the verb: El abuelo no lee el libro. Notice that Spanish doesn't use a helper word like 'does' for negatives; just add no before the action!

If we already know we're talking about the grandfather, could I just say 'He reads the book'?

Yes, you could say Él lee el libro. However, in Spanish, you can often leave out the subject entirely if it's understood from context. So, you can simply say Lee el libro and it means 'He reads the book'.

Why does el not have an accent mark here? I thought I saw it with an accent before.

You are likely thinking of él, which means 'he'. Here, we are using el without the accent, which is the masculine word for 'the' (used for abuelo and libro). They sound exactly the same, but the accent mark tells you which one is being written!