Here's a little information on what records are available and how the research is done. The parish archives were kept at the vicarages and some of them have been ravaged by fire over the years (many houses were built from wood, and of course they were always illuminated with candles), but still very much information has been preserved. In the 1940s or 1950s, Mormons asked for permission to photograph many Swedish church records to incorporate them in their genealogy resources in Salt Lake City. They were allowed to do so provided that they made a copy for the Swedish archives. These microfilms have then been copied (today microcards are used) and are available in a few places in the country plus they can be had through interlibrary loan anywhere in the country. So today there's hardly any risk of loosing church records through fires. But there are also other kinds of archives that may be of interest to genealogists and researchers, and many of them haven't been copied this way. As late as in 1996, the county library in Linköping was completely destroyed by a fire and so was their archive of old manuscripts and documents - and these hadn't been copied.
The Church Law of 1686 stated that the clergy had to keep records of Births, Christenings, Marriages, Deaths, and Burials in the parish, as well as records of who moved to or from the parish. Some bishops had taken similar initiatives early in the 1600s so some records go even further back. Date (or at least year) and place of birth are given in most records, and Birth/Christening records also give the parents' names and names of witnesses (godfathers and godmothers) and often where they lived. On the other hand, I've seen 18th century marriage records where the clergyman didn't even bother to note the date of the marriage - the marriages were just listed in the order they took place (but at least the current year was written as a heading above).
The practice of keeping parish records came from Germany, but the Swedes took it one step further. Here, the clergy not only had to record births, marriages and deaths; they also had to keep records of whether people could read and if they had sufficient knowledge of religion. These records are unique for Sweden and Finland (Finland belonged to Sweden from Medieval times until the Finnish war 1808-1809, when it was taken by Russia), and they are called Husförhörslängder (=Household Examination Rolls). Each year, everyone was examined by the clergyman in their knowledge of religion and reading, and their grades were registered in the Household Examination Rolls. All the persons in the parish were listed, household by household, and their names, date of birth, grades, and some additional information was noted. The records were kept in large books, usually using one spread per household, and they were updated each year for about five or ten years, and then they started on a new volume. When people died or moved, their name was crossed out and the date and reason of their deletion was noted. The list of the household covered not only the family, but also any employees or relatives living with them. There may have been not only the parents and their children but also a couple of farm-hands, a maid, and old grandpa. To the genealogist, the Household Examination Rolls are very valuable as they provide a relatively easy way of finding e.g. all the children of a certain family without having to read the Birth Records from cover to cover (even a baby that died a few days after the birth may be recorded, though some early records only noted the children that were above 15 years of age). The Household Examination Rolls are an excellent source of information, especially during the 19th century. By that time the clergy used special books with pre-printed columns and headers and lines, so they're usually very systematical and readable. In many cases there are Household Examination Rolls from the late 18th century too, but they were written in blank books, often in a very small hand, and with a minimum of information provided.
There are also medieval records of church accounts, there are tax lists since the 1630s (though not complete as noblemen were relieved from taxes), there are deed books for farms that paid taxes back to the 16th century, court records at least since the 17th century, and detailed estate inventories covering every item, no matter how insignificant, owned by the deceased. Of course much of these records are incomplete.
When I started to research Vendela's family, I had been given some facts, and first of all I started checking which of these were correct. She was not born in Osby, Skåne, nor in Linköping, Östergötland. But I had also got the date and place of her marriage (Mogata, Östergötland) and they had proved to be correct. Now grandma told me that marriages were usually held in the parish where the bride lived. I went to the Birth Records of Mogata and found Vendela there. I also noted that the correct date of her birth was March 2, not March 3. I was lucky in that the marriage record also had a reference to a page in the Household Examination Rolls - page 453 in this case (I'd rather not have to read through such a volume searching for a person). At that page, I found her name, the names of her sisters and mother, and the name of her deceased father. There was also the name of an old widow, who might be Vendela's grandmother. The date and parish of each family members' birth was also given (though it's often hard to make out what it says). Now I knew that her mother was from another parish, Kuddby, but her father from Mogata, and that all sisters were born in Mogata. I confirmed the dates of birth using the Birth Records. I used an earlier Household Examination Roll to find the family of Vendela's father, and could confirm that the widow was his mother. All birth/marriage/death dates I find in the Household Examination Rolls are checked against the corresponding records to confirm that they are correct - Birth Records etc are more reliable sources than Household Examination Rolls.
As Vendela's father was dead, another man was running their farm. His name was Nils Peter Carlon, which reminded me of a couple of other facts I had been given: Vendela was said to have had the family name of Johansson Carlon (though none of her parents seemed to bear the name Carlon), and she was supposed to have had a nephew named William Carlon who had emigrated to Chicago. When I looked up Nils Peter Carlon's family in the Household Examination Rolls, I found that he had a son named Vilhelm. Now, this match is close enough to be interesting, as many emigrants made slight changes in their names to make them more similar to American names, or to make them more easily pronounceable in English. But was he really Vendela's nephew? Did one of her sisters marry his father? Eventually I found some clues - Vendela's mother's name was very similar to that of the mother of Nils Peter Carlon. Also, both women were born in the same parish in the same year... and Vendela's mother was a widow when she married that man who became Vendela's father. The two women were simply one and the same (I later found more proof of this), so Vendela was the half-sister of Nils Peter Carlon, and Vilhelm was thus her nephew.
I hope this gives you an idea of what the research process may be like. Some other parts of the family, like Vendela's husband and his parents, have proved trickier to trace.