1860 US Census, Murray County, Georgia (link)
at Genealogy Trails
This site has a handy index of the 1860 census for Murray County, Georgia.
To search the actual census, try FamilySearch's census index, which has linked images of the actual census pages. (It requires a free account and log-in. So far, FamilySearch is always free--it's not just a free trial, like Ancestry).
1860 U.S. Census Search for the FamilySearch Census Index
Each census index seems to have its own quirks. I think the 1860 census can be searched for county as well as state. Sometimes the less you fill in the blanks, the better. Some of the indexes, for instance, will fail to return an existing result if you have too much data input (such as sex, gender, etc.) It just depends on how they've indexed that particular census. Using a date range for the age is best. (Instead of birth, 1838, use birth, 1835-1840, etc.; ages in census vary so). DO NOT put names in the relationship fields for 1850, 1860, and 1870 (such as the field for "mother," "spouse," etcetera). Those census years do not recognize relationships of persons in the household. Instead, use the "other person." A word to the wise: these indexes are rife with transcription errors, so be creative with your wildcard searches. For example, on "Headrick" surname searches, I always try: Hedrick, Headrick, He*ck, *drick, H*drick, etc. I vary input, such as "H*drick" (in the surname field) and "Blount," "Tennessee" for county and state; then remove the county if I'm not getting the right results. I have tried searches for the first name, county, and state (without the surname). It usually returns too many results, usually, but not always, and it can help find someone whose surname is badly misspelled. I've rarely tried this, but it might work: become familiar with common transcription errors. The transcribers often have trouble reading the old-fashioned script and cannot tell "s" from "l"; or "r" from "s," "n," etc. Capital "T" with a flourish is often transcribed as "P." Thus, "Thomas," as obvious as that seems to the descendant, might be transcribed as "Phomas."
1870 is one of the worst census years to search. It doesn't state relationships, and FamilySearch does not have it indexed by county. Therefore, adding the county doesn't weed out the results at all. Searching for "Headrick" of "Blount, Tennessee," will turn up all Headricks in Tennessee. It may also turn up "Hedrick," (common alternates), but not "Haedrick" or "Hadrick" or "Hetrick." But for what it's worth, I sometimes find it easier to search census straight from the collection, not from the main page at FamilySearch. Here's the page for 1870 Census Search:
1870 U.S. Census Search for the FamilySearch Census Index
To find the Census search tool for any decade, I usually just search Google for "1880 census search at FamilySearch" or something like that. Ancestry probably has similar tools, but requires an account (not free, except for the trial period); I don't know if they use the same census index.
These wildcard searches have helped me greatly. I was able to find "Jacob Hddrix" and "William Hedrink" this way.
Speaking of transcribers who cannot read the old-fashioned cursive, read about the search for Mary Ann V. (Caylor) Headrick, and the terrible transcription errors on her death record....
Search for Death Record of Pollyan Fredrik.