One nice thing that I found was that Google Translate gives an approximation of how words are pronounced, so in Swedish, Sweden in pronounced like SVAR-ee-yah. It helps to be a bit aware of how things sound.
As with any research, if the researcher can tie into the noble classes, there is a better chance of getting records going much further back and having a better chance of getting reliable documentation. Sweden was one of the countries considered to be of Viking origin. For some time Swedes went east into Russia (Belarus especially, since that means White Russian - and those "Rus" peoples are suspected of having been Swedes who invaded that far inland.) While this is historically interesting, we are more interested in more recent times. There are tales of early monks coming to Sweden in the early 800s, but for all intents and purposes the country has been Lutheran since the mid 1500s. About 1686 a royal decree mandated that ministers record births, marriages and deaths. Also to be included were those who moved into or out of a parish. The ministers were to do these every year.
Genealogically speaking, I found that births and christenings should have been created for each child. Those may well contain parents and godparents names, and possibly the parents ages and the name of the minister who performed the ceremony. This is similar to parish records in many countries. The words for these are Birth (Födde) and baptismal (Dop).
Marriages are also genealogically significant. They will usually contain dates for the wedding ceremony and the banns (a public announcement in a Christian parish church of an impending marriage between two specified persons). They usually will have the residences of the bride and groom as well. You can also sometimes find the parties' ages and their parents' names mention. The words for these are: Marriage records (Vigsel) and banns (Lysning).
Death and burial records will list a death date, burial date and burial place for the decedent. Sometimes it will also includes their ages, cause of death, and perhaps occupation. The word for these records is: (Död)
One good thing to remember that you may find a death record for someone who dies, but does not have a birth or marriage date. But this could prove to be a parent, grandparent, etc. And a map is handy as well, because people could easily walk a couple of miles to be married. Villages could be quite close together, and likely the couple would be married in the bride's church.
Various sources tell us that almost one out of every five Swedes immigrated to elsewhere, so Swedish Emigration Records (records of departure from Sweden) may prove useful. During the Swedish immigration to the United States in the 19th and early 20th centuries, about 1.3 million Swedes left Sweden for the United States. The main attraction was the availability of low cost, high quality farm land in the upper Midwest and of jobs in mechanical industries and factories in Chicago, Minneapolis, and many smaller cities. Reasons to leave Sweden were population growth and crop failures. Swedish migration peaked in the years from 1870-1900. Unfortunately, there are few pre-1866 Swedish emigration records.
So where do you start looking?
Like all research, it depends on if the relatives came over recently or long ago, and if long ago, what kinds or memorabilia the family has kept. But it is always advisable talk to the older relatives and see what they can remember; to check at home for collectibles such as old photos or letters, family Bibles, postcards, etc. My own great-grandfather was born in 1868, and our lives did overlap to the point of talking with him. (Another great-grandfather was born in 1848, but he died before 1900).
The following suggestions will work as well in the old country as well as in North America. There are other places to look - people leave records of their actions, and these can include legal documents, church records, census records, vital records, will and probate records (what if a person dies in the U.S. and leaves money or has relatives with an interest in their estate, back in Sweden?) That has happened. I have seen where the brother of a very old man had died before the local man had, and that brother's children had died as well, leaving that brother's grandchildren with an interest in the uncle's estate. The petition for proving the will showed the names and residences at that time, which is highly valuable genealogically. And remember, naturalization records which can give exact places of origin.
Knowing the place of origin can lead you to the extremely valuable Husförhörslängd (the so-called household examination records). The LDS has a great page explaining the content of them https://www.familysearch.org/learn/wiki/en/Sweden:_Household_Examination_Records_(Husförhörslängder).
There are several links to the LDS copies online. Sources also note that these are available thorugh Archiv Digital, the SVAR web site, the national and regional archives in Sweden, and also Genline (which is choose-able off the in-house start page for online searching in the FHC's.
With the explosion of Internet-accessible digitized and indexed records you might well find clues in old newspapers and obituaries. And "Genline" is a large online collection of Swedish church records that is online.
How were people named? As with other Scandinavian countries, there was a system of patronymic naming; that is, children took their father's first (given) name as their surname and added -sson or -dotter, referring to male and female children respectively. Of course, some took their surnames from the places they lived or from what they did for a living. This can be confusing in research, where for example someone may be called Kjerstin in the birth record, but later is called Stina in another record. In 1901 a law required people to adopt permanent surnames to be passed onto successive generations.
The following books and sites will help you get started on your research. As with everything in these Internet days, they are meant to be illustrative and not exhaustive.
Books on Swedish research
Clemensson, Per. and Kjell Andersson. Your Swedish Roots: A Step by Step Handbook. Provo, UT. Ancestry, 2004.
Johansson, Carl-Erik. Cradled in Sweden. Logan, UT. Everton Publishers, 1977, c1972. (a practical help to genealogical research in Swedish Records)
"Historical Background Affecting Genealogical Research in Sweden." Salt Lake City, UT: LDS Church, 1976. Call # folio CS923.H57 1976.
"Major Genealogical Record Sources in Sweden." Salt Lake City, UT: LDS Church, 1974. Call # folio CS923.M36 1974.
Larson, David U. Sweden Genealogy Genline Workbook: With Online Support. VisitEuropeOnline.com, 2006.
Hart, Anne. Tracing your Baltic, Scandinavian, Eastern European, & Middle Eastern ancestry Online: Finnish, Swedish, Norwegian, Danish, Icelandic, Estonian, Latvian, Polish, Lithuanian, Greek, Macedonian, Bulgarian, Armenian, Hungarian, Eastern European & Middle Eastern genealogy (All Faiths). New York. ASJA Press, 2005.
Gustafson, Robert J., M.S. "Genealogical Lexicon of North European Languages and Latin, containing Danish-Latin-English, Finnish-English-Latin, Finnish-English-Swedish, German-English-Finnish." Rochester, New York, 1988.
Selected Web sites:
http://www.cyndislist.com/sweden/ - Cyndislist is one of my favorites (although not the only hub site), and in this area she has collected over 300 links to help in your Swedish research.
http://www.dis.se/en.html - the English language home page of Foeringen DIS, a computer genealogy society DIS stands for Datorhjälp i Släktforskningen.
http://www.etgenealogy.se/sag.htm - This is the home page of the print magazine, the "Swedish American Genealogist." See also, http://www.augustana.edu/x13918.xml.
http://www.algonet.se/~hogman/swe_genealogy.htm - A general introduction to Swedish research.
Genline - Now part of Ancestry.com, a pay database. Has historical church records, but is also available at Family History Centers for no charge.
http://en.wikipedia.org/wiki/History_of_Sweden#Early_Swedish_history - A history of Sweden including maps, from Wikipedia.
http://www.algonet.se/~hogman/Naming%20practice_eng.htm - A web page that goes into detail about Swedish naming practices.
https://www.familysearch.org/learn/wiki/en/Sweden - The new web version of the older printed guide to Swedish research. Very thorough and worth looking at.
Genealogical Research in Sweden - While hosted by the pay site Ancestry.com, it is free and gives a good overview of starting research.
http://www.rootsweb.ancestry.com/~wgsweden/ - The WorldGenWeb start page for Sweden. https://www.facebook.com/SwedenGenealogy - What would a webliography be without a Facebook link? General interest community. https://familysearch.org/blog/en/swedish-genealogical-conference/ - A web site dealing with a very large (3500 attendees) conference in Sweden dealing with Swedish genealogy. https://www.familysearch.org/learn/wiki/en/Swedish_Genealogical_Word_List - Just what it says, a clickable list of genealogical terms in Swedish. http://www.arkivdigital.net/ - 37 million color images of various kinds of documents such as church records, court records and inventories of estates. Subscription database.
http://www.genealogi.net/engresearch.htm - The Genealogical Society of Sweden, which advertises a for pay research service.