The rule that decides most comma questions
Ask whether the phrase or clause next to the comma is essential to identifying the noun it describes, or whether it's extra detail that could be deleted without losing the sentence's core meaning. If it's essential, no commas surround it. If it's extra, a comma or a pair of commas sets it off.
Test this by physically removing the phrase and reading what's left. 'The scientist who discovered the compound won an award' needs no commas around 'who discovered the compound' if that clause is what tells you which scientist is meant, out of possibly several. But 'Maria Chen, who discovered the compound, won an award' takes commas, because her name already identifies exactly who is meant, and the clause is just extra detail about her.
Two other places a comma is either required or forbidden
A comma is never placed between a subject and its main verb. This trips people up when the subject is long: 'The students who stayed after class to finish the project, received extra credit' is wrong, because 'the students who stayed after class to finish the project' is the full subject and 'received' is the verb, and no comma belongs between a subject and its verb regardless of length.
A comma is required before a coordinating conjunction (and, but, or, so, yet, for, nor) when it joins two complete sentences. 'The bridge was closed for repairs, and traffic was rerouted downtown' needs the comma because both sides are full sentences joined by 'and.' But 'The bridge was closed for repairs and rerouted traffic downtown' does not need a comma, because the second half, 'rerouted traffic downtown,' is not its own complete sentence, it shares the subject 'the bridge' with the first half.
The trap most students fall into
The trap is adding a comma wherever there's a natural pause when reading the sentence out loud, instead of checking whether the surrounding information is essential or extra. Long sentences create a pause before the reader even reaches the true grammatical break, and students place a comma at that pause instead of at the actual essential-versus-extra boundary.
A second common trap is a comma splice: joining two complete, related sentences with just a comma and no conjunction, because it reads smoothly. 'The forecast called for rain, the game was postponed' is wrong even though it flows naturally when spoken. It needs a semicolon, a period, or 'so' added after the comma.
Worked example
Sentence: 'The novel ___ which the author wrote in just six weeks ___ became an unexpected bestseller.' Options: no commas, a comma before 'which' only, commas both before and after the clause, a comma after 'weeks' only.
Ask whether 'which the author wrote in just six weeks' is essential to identifying which novel is meant. The sentence already refers to 'the novel,' a specific, already-identified book, so the clause is extra biographical detail about it, not information needed to identify which novel. That makes it a removable, extra clause, which needs a comma on both sides, matching a pair, not just one side. Test it: 'The novel became an unexpected bestseller' still makes complete sense with the clause removed, confirming it's extra. The answer is commas both before 'which' and after 'weeks.'
How to build speed on this
Stop reading for rhythm and start reading for structure: find the subject and verb of the main sentence first, then check anything sitting between or around them against the essential-versus-extra test. This is slower at first but becomes close to automatic with repetition, because the test only really runs a small handful of comma rules over and over in different sentences.
StudyPebble's comma practice set drills the essential-versus-extra distinction specifically, since it's the rule behind most comma questions on the digital SAT, with an explanation on each question showing which version of the sentence still makes sense with the clause removed.