There are quite a few ways to deploy your Azure website using Visual Studio, but I find the following the easiest.
Create a vanilla website in Azure. This is my destination site where I will deploy all my changes.
Once you have created a website in Azure, try accessing it from your browser.
You should see a welcome page similar to this.
Next step is to make changes and deploy them to your website.
Let’s say you have to change the way your website looks.
Create a new ASP.NET web application using Visual Studio.
Once you have done your changes and are ready to deploy to Azure, navigate to https://manage.windowsazure.com
Find your web app and click on it to go to the dashboard page.
Click on Download the Publish profile link to download the publishing profile file.
Move back to Visual Studio and right click on your web application and click on Publish.
You will find a dialog box like this. Click on Import.
Browse to the publish profile file you downloaded from Azure and import the file. You should see all the details auto populate in the dialog box as shown below.
Click on publish to start the deployment process.
Navigate to your website to see the changes deployed.
Continue this process for continuous deployment from Visual Studio.