The following example will show all available tables in a listbox.
Put a listbox, a button and a TASQLiteDatabase component on your form. Setup the correct database. Add the below code to the onclick event of your button:

procedure TForm1.Button1Click(Sender: TObject);
begin
 DB.GetTableNames(ListBox1.Items, true);
end;

The following example will create a full data-aware tablegrid on your form.
Create a new application, put a TASQLiteDatabase and a TASQLiteTable component on your form. Apply the correct database to the database component. Apply the TASQLiteDatabase component on the TASQLiteTable. Select the table to create the grid for. Add a TDataSource component, a TDBGrid and a TDBNavigator component on your form. Connect these components to eachother in the useual way (TTable to TDataSource, TDBGrid to TDataSource and TDBNavigator to TDatasource). Set the Active property to 'true'

no code is necessary.

The following example will create a full data-aware tablegrid on your form where the user can enter the tablename.
Create a new application, put a TASQLiteDatabase and a TASQLiteTable component on your form. Apply the correct database to the database component. Apply the TASQLiteDatabase component on the TASQLiteTable. Add a TDataSource component, a TDBGrid and a TDBNavigator component on your form. Connect these components to eachother in the useual way (TTable to TDataSource, TDBGrid to TDataSource and TDBNavigator to TDatasource). Put an edit field for the tablename on your form (with the first example you can also use a pulldown list). Put a button to start the dialog on the form and apply the next code to the onclick event of the button.

procedure TForm1.Button1Click(Sender: TObject);
begin
 ASQLiteTable1.TableName := 'MyTable';
 ASQLiteTable1.Open
end;

The following example will select data from a table using parameters, obtained from a form
Create a new application, put a TASQLiteDatabase and a TASQLiteQuery component on your form. Suppose you want to select a name from the edit field then you should put an edit field on your form. Apply the correct database to the database component. Apply the TASQDatabase component on the TASQTable. Add a TDataSource component and a TDBGrid component on your form. Connect these components to eachother in the useual way (TTable to TDataSource, TDBGrid to TDataSource). Put an edit field for the search criteria on your form. Put a button to start the dialog on the form and apply the next code to the onclick event of the button.

procedure TForm1.Button1Click(Sender: TObject);
begin
 with ASQLiteQuery1 do begin
   close;
   SQL.Clear;
   SQL.Add('select * from mytable where name like %:name');
   Params[0].AsString := Edit1.Text
   Open;
 end;
end;