Is it possible to connect to a DBF file whose path is entered on a form?

The answer depends on how you need it, and what you are going to do once you get the data.  You can use an OleDbConnectionStringBuilder, set properties on the builder, and get a valid connection string.

http://msdn.microsoft.com/en-us/library/system.data.oledb.oledbconnectionstringbuilder.aspx

using System.Data.OleDb;

class Program
{
    static void Main(string[] args)
    {
        OleDbConnectionStringBuilder builder = new OleDbConnectionStringBuilder();
        builder.ConnectionString = @"Data Source=C:\Sample.mdb";

        // Call the Add method to explicitly add key/value
        // pairs to the internal collection.
        builder.Add("Provider", "Microsoft.Jet.Oledb.4.0");
        builder.Add("Jet OLEDB:Database Password", "MyPassword!");
        builder.Add("Jet OLEDB:System Database", @"C:\Workgroup.mdb");

        // Set up row-level locking.
        builder.Add("Jet OLEDB:Database Locking Mode", 1);

        Console.WriteLine(builder.ConnectionString);
        Console.WriteLine();

        // Clear current values and reset known keys to their
        // default values.
        builder.Clear();

        // Pass the OleDbConnectionStringBuilder an existing 
        // connection string, and you can retrieve and
        // modify any of the elements.
        builder.ConnectionString =
            "Provider=DB2OLEDB;Network Transport Library=TCPIP;" +
            "Network Address=192.168.0.12;Initial Catalog=DbAdventures;" +
            "Package Collection=SamplePackage;Default Schema=SampleSchema;";

        Console.WriteLine("Network Address = " + builder["Network Address"].ToString());
        Console.WriteLine();

        // Modify existing items.
        builder["Package Collection"] = "NewPackage";
        builder["Default Schema"] = "NewSchema";

        // Call the Remove method to remove items from 
        // the collection of key/value pairs.
        builder.Remove("User ID");

        // Note that calling Remove on a nonexistent item does not
        // throw an exception.
        builder.Remove("BadItem");
        Console.WriteLine(builder.ConnectionString);
        Console.WriteLine();

        // Setting the indexer adds the value, if 
        // necessary.
        builder["User ID"] = "SampleUser";
        builder["Password"] = "SamplePassword";
        Console.WriteLine(builder.ConnectionString);

        Console.WriteLine("Press Enter to finish.");
        Console.ReadLine();
    }
}

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Thanks for the comments and solution.
You said >>The answer depends on how you need it, and what you are going to do once you get the data.<<
Once I have connected a new form will need to list the records in the file. I need to give the user the ability to edit existing records or press a button alongside a selected record and use that record as a template to add a new record. The user then simply makes a few additional changes to the new record. When the user has finished adding/editing records I need to sort the table by a key field and save it before closing the application.
Is this going to be asking too much?

BTW, your instructions connect to an mdb file. Can VB.Net connect to a dbf file?

Brilliant. thank you very much!!!!