If an adult wants to become a Swedish Citizen [1], you have to fulfill the following criteria [2], of which roughly require that you  have lived in Sweden for 5 years, have made a living and stayed out of trouble. In generally, it is a simple process to follow (at least if you are a European citizen, your mileage may vary). However, I have heard from my expat community that the overall process can take several years after submitting you application. To avoid such a long waiting time and reduce the process to about 8 months, the following steps are important.

1. Apply for Swedish citizenship to Migrationsverket [1]
2. Wait for 6 Months
3. If you have not gotten a reply:
   1. Go to Migrationsverket
   2. Search after “”Begäran om att avgöra ett ärende” (Appeal for decision) [3]
   3. Fill in the form and send it to the Migrationsverket to appeal for a decision upon a procedure
4. You will get a rejection of your appeal for a decision (Migrationsverket: “difficult decision, “takes  time”)
   Note: This is a rejection of you appeal to make a (fast) decision, not a rejection of your application for Swedish citizenship.
5. Follow the instructions to appeal the rejection of your appeal for decision.
6. You will get a reply by the court that they told the migrationsverket to speed up their decision making and the decision by the migrationsverket with a (hopefully positive) reply at about the same time.

The overall process (if no other barriers appear) should take about 8 months.

References:
[1] https://www.migrationsverket.se/Privatpersoner/Bli-svensk-medborgare.html

[2] https://www.migrationsverket.se/Privatpersoner/Bli-svensk-medborgare/Ansok-eller-anmal-om-medborgarskap/Medborgarskap-for-vuxna.html

[3] https://www.migrationsverket.se/download/18.1ef19f6e163f45d340aa51/1698676924572/270011_Begaran_avgora_arende_sv.pdf