upload files to Azure file storage from web app using rest api

This piece of code is based on the answer I get from Gary Holland above. I hope other people benefit from it. I am not good at programming, hopefully the code looks ok.

if (FileUpload1.HasFile)
    {
        //Connect to Azure
        CloudStorageAccount storageAccount = CloudStorageAccount.Parse(ConfigurationManager.ConnectionStrings["StorageConnectionString"].ConnectionString);

        // Create a reference to the file client.
        CloudFileClient fileClient = storageAccount.CreateCloudFileClient();

        // Get a reference to the file share we created previously.
        CloudFileShare share = fileClient.GetShareReference("yourfilesharename");

        if (share.Exists())
        {


            // Generate a SAS for a file in the share
            CloudFileDirectory rootDir = share.GetRootDirectoryReference();
            CloudFileDirectory sampleDir = rootDir.GetDirectoryReference("folderthatyouuploadto");
            CloudFile file = sampleDir.GetFileReference(FileUpload1.FileName);

            Stream fileStream = FileUpload1.PostedFile.InputStream;

            file.UploadFromStream(fileStream);
            fileStream.Dispose();


        }
    }

Azure provide a nuget library that you can use to upload, and do other "file management" types of activities on Azure File Storage.

The library is called: WindowsAzure.Storage

UPDATE: The new library to use is Azure.Storage.Blobs.

Here are the basics of getting this going:

//Connect to Azure
CloudStorageAccount storageAccount = CloudStorageAccount.Parse(connectionString);

// Create a reference to the file client.
CloudFileClient fileClient = storageAccount.CreateCloudFileClient();      

// Create a reference to the Azure path
CloudFileDirectory cloudFileDirectory = GetCloudFileShare().GetRootDirectoryReference().GetDirectoryReference(path);

//Create a reference to the filename that you will be uploading
CloudFile cloudFile = cloudSubDirectory.GetFileReference(fileName);

//Open a stream from a local file.
Stream fileStream= File.OpenRead(localfile);

//Upload the file to Azure.
await cloudFile.UploadFromStreamAsync(fileStream);
fileStream.Dispose();

More links and info here (note scroll a fair way down for samples): https://azure.microsoft.com/en-us/documentation/articles/storage-dotnet-how-to-use-files/