We use subordinating conjunctions (subordinators) to introduce subordinate clauses, the main ones being "that", "whether" and "if". The subordinator "that" is used with finite content clauses:
(1) "I agree [that Sue is the best candidate]".
(2) "I wonder [whether the book is still available]".
(3) "They don't know [if you're serious]".
But sometimes the conjunction "that" is optional:
(4) "I know [(that) it's genuine]".
(5) "I realise [(that)you feel insulted]".
And sometimes, especially with adjuncts (adverbials), other subordinators are used:
(6) "Please pick up the dry-cleaning [while you are in town]".
(7) "[When Ed was visiting me], he left his wallet behind".
(8) "I can't go [because it's too expensive]".
(9) "I left early [to get the train]".
That's just a brief explanation, but I hope it will give you an idea of when we use subordinators.