It's done in junior year, so age 16/17ish.
AntsMarching has described it well.
There are coaching courses available - look for books online, and prep courses that may be available are worth looking into too. SAT and ACT prep is quite a cottage industry. There are strategies and keys to tackling certain types of question -- many American hs students do SAT and ACT prep courses and can improve their predicted score by several percentiles. This can make the difference between selective and highly selective school application.
The format is multiple choice in every area except some of the maths.
By junior year, students would be in their third year of high school maths and those on a university-bound track would have taken algebra, geometry and be doing pre-calculus. Some students would already be doing calculus. Some would be doing geometry still. A student who wanted to do well would need to be at a solid pre-cal level in maths (getting B and up in coursework). Calculators are allowed iirc but only those that are calculators only, with no qwerty keyboards or phones and no built in programmes. Find out the specifics though.
The writing sample section tends to be disregarded by selective universities as they require applicants to provide a personal essay with their applications (one in particular included among its choices 'So Where Is Waldo Anyway?' this year) and they trust their own readers better than College Board employees to grade applicant writing.
A student who is running out of time should guess and finish.
The SAT subject tests are different.
(The PSAT is different again and is used to determine eligibility for the National Merit Scholarship Programme and also as a predictor of the SATs. You have to register through your school and the school needs to be registered with the College Board, which administers the exam. It can be a predictor of SAT scores but it's not worth doing as the standard in maths is higher in the SAT.)
There is really no such thing as an 'average American high school diploma' American schools vary incredibly in quality as they are controlled primarily by each individual school district. You really can't say 'An American high school diploma is the equivalent of GCSEs' some would be far worse and some would leave GCSE courses and grades in the dust. From one district to another the standard can vary enormously. The SAT and ACT function to eliminate the guesswork by universities as to quality of high school and reliability of teacher recommendations or high school grades