I would simply use the async methods on WebClient – much easier to work with:
WebClient client = new WebClient();
client.DownloadStringCompleted += (sender,args) => {
if(!args.Cancelled && args.Error == null) {
string result = args.Result; // do something fun...
}
};
client.DownloadStringAsync(new Uri("http://foo.com/bar"));
But to answer the question; assuming it is text, something like (noting you may need to specify the encoding):
using (var reader = new StreamReader(response.GetResponseStream()))
{
string result = reader.ReadToEnd(); // do something fun...
}