The best option is to start searching from your home country. There are many classified sections available on Internet. The main Swedish newspapers, such as Dagens Nyheter or the Swedish newspaper in English, the Local, have classified sections.
You should also be prepared to stay in temporary accommodation, such as a hostel, hotel or guesthouse (depending on your budget) for a short period upon arrival (Sweden’s official site for tourism has a temporary accommodation section). If you are coming with your family, it may be more comfortable for them to arrive after you have found suitable accommodation.
Unless you want to depend on luck, you should consider several options for your apartment search. The most important thing is to have a very clear idea of what you are looking for, otherwise you will waste time. Familiarise yourself with your new environment by walking around, seeing how transport works and asking other people about different neighbourhoods and areas.
There is a wide range of options when looking for an apartment. As ever, the more you’re willing to pay (i.e. using an estate agent or relocation specialist), the easier your search will be.