It's very simple if you follow this doc.
I have a demo as below:
1.In visual studio -> Nuget Package Manager, install the latest version of WindowsAzure.ConfigurationManager and WindowsAzure.Storage
2.In the web.config -> appsettings node, add <add key="StorageConnectionString" value="your storage account string" />:

3.In your asp.net web project, add a custom class derived from TableEntity:
public class CustomerEntity : TableEntity
{
    public CustomerEntity(string lastName, string firstName)
    {
        this.PartitionKey = lastName;
        this.RowKey = firstName;
    }
    public CustomerEntity() { }
    public string Email { get; set; }
    public string PhoneNumber { get; set; }
}
4.Then in your controller, add the following code(I add the code in Contact method):
       using System.Web.Mvc;
       using Microsoft.Azure;
       using Microsoft.WindowsAzure.Storage;
       using Microsoft.WindowsAzure.Storage.Table; 
        public ActionResult Contact()
        {
            //define the emails to output in web page
            string emails = "";
            // Retrieve the storage account from the connection string.
            CloudStorageAccount storageAccount = CloudStorageAccount.Parse(
                CloudConfigurationManager.GetSetting("StorageConnectionString"));
            // Create the table client.
            CloudTableClient tableClient = storageAccount.CreateCloudTableClient();
            // Create the CloudTable object that represents the "people" table.
            CloudTable table = tableClient.GetTableReference("people");
            TableQuery<CustomerEntity> query = new TableQuery<CustomerEntity>();
            foreach (CustomerEntity entity in table.ExecuteQuery(query))
            {
                    emails += entity.Email+";";
            }
            ViewBag.Message = "Your contact page."+emails;
            return View();
        }
- My azure table and the test result:
 
all the email addresses are displayed in web page:
