In case of illness, you should go to your local health centre (Vårdcentralen), which provides doctors, nurses and other specialists. Primary care used to be relatively low in Sweden. However, primary care physicians (equivalent of a GP) are now the norm. You will have no problem to find a doctor in Sweden as all municipalities have a health centre. For information you can call the 24h non-emergency health number 1177.
Consultations at a primary care physician or specialist are not free in Sweden. Every patient has to pay an out-of-pocket fee. However, this fee is very low, most of the cost being subsidised by the State. The cost will vary between SEK 100 and 150, depending on your county. The amount you have to pay directly for healthcare is limited by a SEK 900 ceiling during each 12 month period. If you are a citizen of the EU/EEA and have a European healthcare card (which certifies you contribute in your home country) you will be covered in the same way as a Swedish citizen. If you are not from the EU/EEA and that your country has no agreement with Sweden, you should take a private travel insurance covering your stay in the country as you will have to cover the costs of medication and treatment. A normal GP visit will cost around SEK 1,700-2,000 if not covered by insurance.
There are sixty hospitals in Sweden providing 24 hour emergency services. Eight of these are regional and offer specialised services. In some counties, private hospitals are contracted but are not allowed to offer private healthcare. You will still be covered by the healthcare system (if you are a long-term resident or Swedish). The fee per day in a hospital is SEK 80. Outpatient care pricing is regulated by the county council. Waiting lists in hospitals tend to be short, although there are complaints for non-urgent treatments such as cataract or hip replacement surgery.
Dental care is free in Sweden for persons under 20 years old. After this age, dental care is paid by the patient although the state reimburses around 10-15% of the total cost. For persons older than 65 the cost paid by the patient is capped at SEK 7800, plus the cost of materials and implants.