You haven't given enough info to answer that question - there are many different ways to make a database.
For the simplest - a "flat file", you have one or more data files, that are accessed by your program, as needed. If the amount of data is quite small, it may be loaded into memory, but probably, at least parts of it, will be accessed through files.
Any way you go, you'll need to have functions to search, sort, display, add and delete (usually just a zero out of a name or ID number and name), or re-size (compress), the data. The search and sort need to handle multiple and single entries, (group searches), and sort by multiple keys. (via pointer or index arrays, no data is really sorted, it just looks that way).
Some types might include:
1) "roll your own". ;)
2) MS Access (full or just a helper) for Access
3) MySql lite
I'm sure there are others. In C, you usually use structs to group the different characteristics (members and fields), of the record. Data is handled via binary mode reads and writes, of those records and/or fields.
BEFORE you post back for further info, post up YOUR program and let's talk specifics about that. Databases are a BIG topic, and unsuited for long forum posts. There is a lot of info available on the net.