Learn Hardcore Latin: Lucia signum parvum in margine ponit. - Lucia puts a small mark in the margin.

Lucia is the subject because it is in the nominative singular, the case normally used for the doer of the action. Also, ponit means he/she/it places, so the verb is singular and matches Lucia as a single subject.

Why is signum the object?

Signum is the direct object, the thing being placed. It is in the accusative singular, which is the case Latin commonly uses for the direct object.

So in this sentence:

Lucia = the one doing the action
signum = the thing being placed

Why is it signum parvum and not parvus signum?

Because parvum has to agree with signum in gender, number, and case.

signum is neuter
singular
accusative

So the adjective must also be neuter singular accusative: parvum

That is why you get signum parvum = a small sign/mark

Parvus would be masculine nominative singular, so it would not match signum.