The part of the grammar page this lesson drills — read it here, then use it.
Coordinating conjunctions - и, а, или, али
И (and) simply adds one thing after another with no contrast implied: Волим кафу и чај. (I like coffee and tea.) А also translates as and, but it specifically contrasts two things placed side by side: Ја пијем кафу, а он пије чај. (I drink coffee, and/whereas he drinks tea.)
Или (or) offers a choice: Хоћеш ли кафу или чај? Али (but) is a stronger contrast than а - it overrides an expectation rather than just placing two facts side by side: Уморан сам, али идем на посао. (I'm tired, but I'm going to work.)
Subordinating conjunctions - да, јер, ако, кад(а)
Да (that/so that) introduces a subordinate clause: Мислим да си у праву. (I think that you're right.) Crucially, да + the present tense also replaces the infinitive after verbs like желети (want), морати (must) and моћи (can): Желим да учим српски. (I want to learn Serbian), not the grammatical but overwhelmingly avoided Желим учити.
Јер and зато што both mean because and are interchangeable: Не долазим јер сам болестан. Ако (if) introduces a condition and кад(а) (when) introduces a time: Ако имаш времена, дођи. (If you have time, come.) Кад дођеш, јави ми се. (When you come, let me know.)
Special cases
Зато alone means therefore/that's why, not because - don't confuse it with зато што (because), which functions like јер.
Да + present tense replacing the infinitive is not an optional stylistic flourish - it is the overwhelmingly dominant, standard construction in modern Serbian, even though the infinitive itself remains grammatical.