Common conjunction slips
Ten minutes on the topic's own four common mistakes: и reached for where a contrast needs а, a bare infinitive left after желети instead of да + present, зато alone used for because instead of јер, and a concession left with plain а instead of the stronger али. Build sentences around finishing something, catching each slip in turn, before the unit's own listening and reading put the whole topic to work.
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.