Learn Finnish: Opettaja näyttää kuvan opiskelijalle. - The teacher shows the picture to the student.

We add the ending -lle to the word opiskelija (student), making it opiskelijalle. This is called the allative case, and it often translates to "to" someone or "onto" something. If you wanted to ask "to whom" the teacher shows the picture, you would use the question word kenelle.

Why does the word for picture (kuva) have an -n at the end?

The -n ending shows that kuvan is the object of the sentence—the thing being acted upon. In Finnish, objects often take this ending to show that the action is complete or covers the entire object. The teacher is showing the whole picture.

The verb näyttää (shows) looks exactly like its dictionary form. Why is that?

To make the "he/she/it" (3rd person singular) form, Finnish adds an extra copy of the last vowel to the verb's stem. The stem here is näyttä-, so adding another ä makes it näyttää. It just happens to look identical to the basic dictionary form!

Could I use oppilaalle instead of opiskelijalle?

Yes, but it changes the context slightly. Opiskelija is usually an older student, like someone in university or an adult language course. Oppilas refers to a younger pupil in primary or middle school. If the teacher is showing a picture to a young child, oppilaalle would be the right choice.