Learn Polish: Jestem dobrym studentem.

In Polish, the verb ending usually tells you who is doing the action. Jestem means "I am", so adding ja at the beginning is unnecessary unless you want to add special emphasis.

Why is the word for student studentem instead of just student?

This happens because of the verb być (to be). When you use this verb to state someone's profession, nationality, or identity, the noun that follows takes a form called the Instrumental case. For most masculine nouns like student, you add -em, making it studentem.

Why is the adjective dobrym instead of dobry?

In Polish, adjectives must always match the grammatical form of the noun they describe. Because studentem is in the Instrumental case, the adjective must be as well. For masculine adjectives, the ending changes from -y to -ym, turning dobry into dobrym.

Does this sentence tell us if the speaker is male or female?

Yes, it tells us the speaker is male. A female student would use the feminine word studentka. In the Instrumental case, feminine words take an -ą ending, so a woman would say Jestem dobrą studentką.