If you are looking for cases pertaining specifically to Ohio, there are three basic search strategies:
1. Search by citation
2. Search by case name
3. Search by keyword/subject
See sections below for more information on each of these types of searches.
If you have a legal citation, you will need to correctly identify each component to determine which reporter published your case. Each citation is typically broken down into three basic components: the volume number; the reporter series; the page number.
For example: 89 Ohio St. 93
89→ Volume # 89
Ohio St.→ Ohio State Reports
93→ Page # 93
Once you have deciphered the citation, you can use various resources to locate your case.
To search for Ohio Supreme Court and appellate decisions on the Ohio Supreme Court's website by citation you can use the WebCite number. This is a new universal citation method adopted by many states to locate cases online.
For example: 2014-Ohio-3365
Ohio --> State
3365 --> Unique number
If you have a case name (names of parties involved), there are several sources available that will enable you to locate the case.
Shepard's (Lexis) , Keycite (Westlaw) and B-cite(Bloomberg) list subsequent cases that cited the case in question, and whether the subsequent case overruled or followed the case in question. In order to make sure a case is "still good law", don't stop at Shepard's or Keycite or Bcite.
It is possible the case is no longer good law, but no subsequent case ever cited that case as overruled. Looking at the Table of Authorities in Lexis or Westlaw will help determine whether the underpinning cases cited in a decision have been overturned. Table of Authorities is included in Bcite results. In LexisAdvance, Legal Issue Trail lists cases cited in that legal passage, and gives Shepards signals for those cases, providing the same functionality as table of authorities.
Thorough research of a question through electronic searches and/or secondary sources should reveal any changes in the law.
Additionally, you should also check the statutes to see if the case was overruled by statute, although Shepards and Keycite often reflect when a case is overruled by statute.