Select a free course that appeals to you. There are several online. The Stockholm School of Economics offers a beginner's course at www2.hhs.se/isa/swedish/. This course includes basic conversational and reading skills. Language teacher Björn Engdahl also offers an online course in basic Swedish for free at www.onlineswedish.com/main.php. This course covers basic vocabulary and grammar, plus irregular verbs, and has a self-testing section. Indo-European Language Tutorials also offers a free basic course in Swedish at www.ielanguages.com/swedish.html.
Improve your vocabulary with online dictionaries and practice with flashcards. Online Swedish-English/English-Swedish dictionaries can be found at http://lexin.nada.kth.se/sve-eng.html and http://www.foreignword.com/dictionary/Swedish/. You can find online flashcards and vocabulary builders at www.omniglot.com/writing/swedish.htm.
Practice online with Language Exchange (www.mylanguageexchange.com/learn/Swedish.asp). This service pairs you up with native speakers so that you can practice speaking, hearing, writing and reading Swedish through voice chat and text chat. According to Language Exchange, this method enables you to learn "the real Swedish language (slang, expressions, etc.) used by ordinary native speakers, [get] accustomed to the way native speakers speak in real (casual) Swedish conversation; [and] make a friend in the Swedish-speaking culture."
Read books in Swedish from the University of Virginia at www.lib.virginia.edu/wess/etexts.html#swedish to improve your reading comprehension and vocabulary.