Especially if you have an older home, you must think so many different thoughts: What were the life stories of those who lived in the house before you? How old is the house, and what additions were added to the original structure? How old is the roof, the plumbing, etc.? Sometimes the style of the house will give you clues as to its approximate age.
The easiest way to get started is to go to your county courthouse and tax appraiser's office with your legal description from your tax bill and ask for copies of any pertinent documents that will give you a list of former owners (deeds, wills, mortgages, and probate records), etc. If there was a big increase in a selling price along the way, that is a good indication that some type of large addition was added. Just remember to ask what the cost will be for the copies so that you aren't shocked at the total.
Some older maps, city directories (which might also list occupations), census records, insurance maps, or pictures may give an idea of what the property looked like in the past and who lived there. You might be able to find this information in your local library or historical society's records. Also, the library or local newspaper may have microfilm archives that would be of help. In the nineteenth century the Library of Congress catalogued lithographs with an accurate view of every existing building in a town at the time of the creation of the lithographs.
From the above information you can compile a list of former owners and can then check your local area's telephone book (especially if you are in a smaller city) to see if they or perhaps some of their relatives are still in the area. You may get lucky and be able to find some people who can give you interesting background stories on your home. Just remember that not everyone will want to talk about it, and you have to respect their privacy.
Of course there are also publication and online sources that might be able to help. A fascinating free online one is thatsmyoldhouse.com which is well worth a look.
Preserve old delicate documents plus the history that you eventually put together in clear archival covers (available at crafts, scrapbook, or stationery stores). Put those into binders for the enjoyment of you and your heirs.