The little word kad (that) is used to connect one statement to another:

Vytautas sako, kad Laimis rašo knygą. Vytautas says that Laimis is writing a book.
Tėvas sako, kad tu jo neklausai. Father says that you don't listen to him.

Laimis rašo, kad yra pamokoje. Laimis is writing that he is in the lesson.
Milda skaito, kad jos mokytojas yra Italijoje. Milda is reading that her teacher is in Italy.

Ji tiki, kad aš esu pamokoje. She believes that I am in the lesson.
Mes tikime, kad tu perki kompiuterį. We believe that you are buying a computer.
Gali nesakyti: aš tikiu, kad tu turi kompiuterį. You don't have to say: I believe that you have a computer.

You cannot skip kad as freely as you can skip that in English:

Jis tiki, kad mums reikia eiti tiesiai. He believes (that) we need to go straight ahead.

However nowadays, due to the influence of English, you can sometimes skip kad in frequently used constructions such as "manau, kad":

Manau, mums reikia eiti tiesiai. I think we need to go straight ahead.