For that you would want to use the OpenFileDialog class with the Multiselect property set to true:
string destination = @"c:\programfiles\myfolder";
OpenFileDialog ofd = new OpenFileDialog();
ofd.Multiselect = true;
if (DialogResult.OK == ofd.ShowDialog()) {
foreach (string file in ofd.FileNames) {
File.Copy(file, Path.Combine(destination, Path.GetFileName(file)));
}
}