How can I get the field names of a database table?

Use IDataReader.GetSchemaTable()

Here's an actual example that accesses the table schema and prints it plain and in XML (just to see what information you get):

class AccessTableSchemaTest
{
    public static DbConnection GetConnection()
    {
        return new OleDbConnection("Provider=Microsoft.Jet.OLEDB.4.0;Data Source=..\\Test.mdb");
    }

    static void Main(string[] args)
    {
        using (DbConnection conn = GetConnection())
        {
            conn.Open();

            DbCommand command = conn.CreateCommand();
            // (1) we're not interested in any data
            command.CommandText = "select * from Test where 1 = 0";
            command.CommandType = CommandType.Text;

            DbDataReader reader = command.ExecuteReader();
            // (2) get the schema of the result set
            DataTable schemaTable = reader.GetSchemaTable();

            conn.Close();
        }

        PrintSchemaPlain(schemaTable);

        Console.WriteLine(new string('-', 80));

        PrintSchemaAsXml(schemaTable);

        Console.Read();
    }

    private static void PrintSchemaPlain(DataTable schemaTable)
    {
        foreach (DataRow row in schemaTable.Rows)
        {
            Console.WriteLine("{0}, {1}, {2}",
                row.Field<string>("ColumnName"),
                row.Field<Type>("DataType"),
                row.Field<int>("ColumnSize"));
        }
    }

    private static void PrintSchemaAsXml(DataTable schemaTable)
    {
        StringWriter stringWriter = new StringWriter();
        schemaTable.WriteXml(stringWriter);
        Console.WriteLine(stringWriter.ToString());
    }
}

Points of interest:

1. Don't return any data by giving a where clause that always evaluates to false. Of course this only applies if you're not interested in the data :-).
2. Use IDataReader.GetSchemaTable() to get a DataTable with detailed info about the actual table.

For my test table the output was:

ID, System.Int32, 4
Field1, System.String, 50
Field2, System.Int32, 4
Field3, System.DateTime, 8
--------------------------------------------------------------------------------
<DocumentElement>
  <SchemaTable>
    <ColumnName>ID</ColumnName>
    <ColumnOrdinal>0</ColumnOrdinal>
    <ColumnSize>4</ColumnSize>
    <NumericPrecision>10</NumericPrecision>
    <NumericScale>255</NumericScale>
    <DataType>System.Int32, mscorlib, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</DataType>
    <ProviderType>3</ProviderType>
    <IsLong>false</IsLong>
    <AllowDBNull>true</AllowDBNull>
    <IsReadOnly>false</IsReadOnly>
    <IsRowVersion>false</IsRowVersion>
    <IsUnique>false</IsUnique>
    <IsKey>false</IsKey>
    <IsAutoIncrement>false</IsAutoIncrement>
  </SchemaTable>
  [...]
</DocumentElement>

this will work on sql server 2005 and up:

select * from INFORMATION_SCHEMA.COLUMNS 
where TABLE_Name='YourTableName'
order by ORDINAL_POSITION

Run this query:

select top 1 *
From foo

and then walk the list fields (and returned values) in the result set to get the field names.