Yes, you should provide a source for the information you submit. You can use personal knowledge, family records, letters of correspondence, and so forth, as legitimate sources. You are strongly encouraged to provide as much source information as possible for each name and event you contribute.Contrast that statement with the 885 page book by Elizabeth Shown Mills:
See Attaching historical records to an entire family (72210) for ways to attach images of sources, such as census records and birth records.
Mills, Elizabeth Shown. Evidence Explained: Citing History Sources from Artifacts to Cyberspace. Baltimore, Md: Genealogical Pub. Co, 2007.
and you can begin to see that there is a huge gulf between the bare concept of adding a source and reality of sources and source citations in the more professional realms of family history. I must say, however, that I tend more towards having sources tell rather simply where you or someone else can find the source of the information you submit rather than dwelling on the issue of formatting formal citations. Unfortunately, the default in Family Tree is to submit information without a source at all.
I find it interesting that the "academic" and formal journal citations dwell so heavily on format and on standardized content that they often fail to tell where the information might be found. This is not particularly true for entries concerning Internet sources because the URL suffices, but in most cases citations to books and other printed material gives the book reference but not the place where the book can be found either online or in a library or other archive. I fear that I am guilty of doing this myself. An alternative is to always give a link to the entry in WorldCat.org or at least the OCLC number for the item.
The Help Center for FamilySearch Family Tree also has a "Tips" section. The Tip about sources is entitled, "FamilySearch Family Tree Tips for Adding Sources." Here is that tip:
To search Historical Records and find sources for a person, under Research Help, click Search Records. Family Tree searches Historical Records with the first name, last name, birth year range, and birthplace from the Person page (if available). A new browser window or tab displays possible matching records.
To attach a historical record you've found as a source, click Attach to Family Tree.Yes, it can be that simple. Of course there is a catch. You have to make sure that the "source" found by FamilySearch really refers to your ancestors. The link to the historical records under the Research Help links will automatically add a source citation to your ancestor if you attach the record. But what about records and sources from other websites or libraries or archives etc?
This is where the system becomes strained. It is not enough to say that the record came from Ancestry.com or MyHeritage.com, it is also important to give enough information so that the search for the record can be duplicated. This is especially true of sources found in other websites. In addition to a link to the actual item, the rest of the description of the record should also be included in case the link is broken for some reason.
Although it may seem unnecessary to the new family historian, adding sources is one of the main ways that the Family Tree program will become a believable resource.