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.
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Once you have created a website in Azure, try accessing it from your browser.
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You should see a welcome page similar to this.
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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.
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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.
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Click on Download the Publish profile link to download the publishing profile file.
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Move back to Visual Studio and right click on your web application and click on Publish.
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You will find a dialog box like this. Click on Import.
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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.
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Click on publish to start the deployment process.
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Navigate to your website to see the changes deployed.
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Continue this process for continuous deployment from Visual Studio.