Good methods...
First, know your family.
-- Were they mobile during reconstruction?
-- Did they own land in the area in which they lived in 1870?
-- When did they buy and from whom?
-- Were there other family members in the same area?

Then, know available resources.
1. Voter's registrations (some gave additional information on birthplace, years in the county, prior residence, 'moved to ...')

2. Marriage Records

3. Tax records

4. Deeds / Land Records

5. Wills/Probates/ Successions (division of property)

6. Local newspapers of the era

7. Records of Southern Plantations from Emancipation to the Great Migration

8. Southern Claims Commission

9. Serial Sets (Congressional Records)

10. Civil War Military Records

11. Freedmen's Bank Records

12. Freedmen's Bureau Records

etc...

But one of the most important reconstruction era resource is the Ninth Census of the United States (1870).

Much can be learned by studying the different schedules, as David suggests.
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Schedule No.1 – General Population Schedule.

Schedule No.2 - Mortality. This schedule collected data on persons who died during the year.

Schedule No.3 - Agriculture.