The two main dbExpress components are TSQLConnection and TSQLDataset.
TSQLConnection provides the mechanism to connect to (and disconnect from) a database. Drop the TSQLConnection components on your form and double click to open a dialog box where you can specify details of the database and the means to connect to it.
You can also use the TSQLConnection component to send SQL statements to the database providing they do not return a result set. Typically, these SQL statements would be CREATE, DROP and so on.
TSQLDataset provides the means to send SQL statements to the database which do return a result set. Typically, these are SELECT statements. An important consideration is that the returned result set is unidirectional.
There are other dbExpress components. These are TSQLTable, TSQLStoredProc, TSQLQuery and TSQLSimpleDataset. The first three provide some kind of compatibility with TTable, TStoredProc and TQuery to assist conversion from a BDE application. They are not intended to be used in new applications.