Contracting in Sweden
If you are an EU citizen, you don't need a work permit to work in Sweden. However, if you intend to stay as a resident in Sweden for more than 3 months while you work then you do need to apply for a residence permit.
You can apply for the permit before you plan to start work, but you can reside and work in Sweden (for up to three months) before you need to apply for a permit. The permit itself can take up to six months to be processed but you are allowed to stay while it is processing.
To apply for a residence permit you need to fill out this form and enclose a copy of your passport and a signed declaration from your employer / client describing your work and the duration of your stay.
Paying for services in Sweden can be a bit of a headache unless you have a Swedish bank account. Getting a bank account first requires getting a person-number which you also have to apply for.
To transfer money internationally, you need an IBAN number and a BIC code (or swift code) for the bank account, bank, and country. You also need the name and address of the bank you want to transfer to, and the name of the account into which you are paying. There is a fee, it can take 7 working days or more, and you get no guarantees that the money you send will even arrive at all. This is a real con and the banks need to get this sorted out. I personally can make and accept payments at the click of a button with PayPal - why this is so much hassle for the banks I have no idea...
Sweden has no official language and most Swedes are multi-lingual. Almost everybody speaks at least Swedish and English and they can happily mix the two within a single sentence. However, writing is fairly exclusively in Swedish. Most of the products available in shops in Sweden are written in Swedish first, then Finnish and Norweigen, and then other languages sometimes including English.