You can use the SaveFileDialog like this:
SaveFileDialog sfd = new SaveFileDialog();
sfd.Filter = "Images|*.png;*.bmp;*.jpg";
ImageFormat format = ImageFormat.Png;
if (sfd.ShowDialog() == System.Windows.Forms.DialogResult.OK)
{
string ext = System.IO.Path.GetExtension(sfd.FileName);
switch (ext)
{
case ".jpg":
format = ImageFormat.Jpeg;
break;
case ".bmp":
format = ImageFormat.Bmp;
break;
}
pictureBox1.Image.Save(sfd.FileName, format);
}