The below code will do so
Public Function GetBlobData(filename As String, connectionString As String, containerName As String) As String
' Retrieve storage account from connection string.
Dim storageAccount As CloudStorageAccount = CloudStorageAccount.Parse(connectionString)
' Create the blob client.
Dim blobClient As CloudBlobClient = storageAccount.CreateCloudBlobClient()
' Retrieve reference to a previously created container.
Dim container As CloudBlobContainer = blobClient.GetContainerReference(containerName)
' Retrieve reference to a blob named "test.csv"
Dim blockBlob2 As CloudBlockBlob = container.GetBlockBlobReference(filename)
Dim text As String
Using memoryStream = New MemoryStream()
blockBlob2.DownloadToStream(memoryStream)
text = System.Text.Encoding.UTF8.GetString(memoryStream.ToArray())
End Using
Return text
End Function