★★★ An extended and updated version of this post is over at Sweden For Real. ★★★

Mandatory (paperwork, tests, riskutbildning):
Synintyg (eye test): around 150:-
Riskettan: around 700:-
Risktvåan: around 2000:-
Test, theory: from 325:- to 400:- (more expensive in the evening and on the weekend)
Test, practice: from 800:- to 1040:- (more expensive in the evening and on the weekend)
Car for the test: 400:- from Trafikverket, around 700:- from a driving school
Photo for the license: 80:-
Manufacturing of the license: 250:-
Sum of the mandatory part: at least 4705:-

Optional, but not really (learning):
Theory book: around 300:-
Practice online with theory questions: around 250:-
Driving lessons: 10-30 × 1000:-

Optional (for the path without a driving school):
Handledarutbildning (the special training for the driver who’ll teach you): 350:-

So the driving school path from complete scratch is at least 15255:-, if you learn fast, and the "learning from a friend" path is at least 5055:-.

It might also be wise to allow for a repeat test when calculating costs or planning your life as a future driver. It is pretty easy to fail the practice test, for example if you just appear too insecure. The statistics for the tests can be found on Trafikverket’s website, but for example in the period of January–September of 2019 the odds were like this:

Theory (first attempt)
Total number: 103422
Applied privately: 47291
Applied through a school: 56131
Success rate, total: 65.16%
Success rate, private: 49.90%
Success rate, through driving school: 78.03%

Practice (first attempt)
Total number: 101875
Applied privately: 45918
Applied through a school: 55957
Success rate, total: 53.91%
Success rate, private: 34.76%
Success rate, through driving school: 69.62%

Second attempt can be booked if you fail the first one, and costs just as much.