http://www.skatteverket.se/privat/sjalvservice/blanketterbroschyrer/broschyrer/info/345b.4.353fa3f313ec5f91b95353.html

One of the most important things you will need in Sweden is a personal ID number (personnummer). You will need it to be recognized by Swedish administration and authorities, to pay with a credit car, and enter to contracts. The Swedish Tax Authority (Skatteverket) issues personal ID numbers. You can apply at your local tax office. When applying every member of the family needs to present. You will need your work/resident permit, passport, and civil status documents such as birth and marriage certificates. You should receive your personal ID number within 4-10 days. Once you have it you can apply for an ID Card at your local Skatteverket office. See requirements and more information in English at:

http://www.skatteverket.se/servicelankar/otherlanguages/inenglish/individualsemployees/idcard.4.76a43be412206334b89800039548.html