To publish your website over Microsoft azure web app just follow the below steps

Prerequisites : -
1) Azure account with active subscription - here 
2) Sample Website - you can use this sample 

Step 1 - Login into Azure Account and Click on New button on Left navigation bar

Step 2 - Click on Web + Mobile and then click Web App option

Step 3 - Enter your desired Unique App name , Suscription , Resource group ,  and App service plan/Location And Click on Create

Now your web app is deploying you can see its progress status in notification bar 

Step 4 - With in few minutes your website will be deployed. Now, click on "Go to Resource" button in notification bar to navigate to your deployed App

Step 5 - Click on Get published button on the ribbon to get the Publisher setting of your Web App

Step 6 - Keep/Save the published file in your system (it will be used in further steps) 

Step 7 - Now open your web project that you want to publish in Visual studio -> right click on it -> click on publish option

Step 8 - A Dialogue will appear click on Import option

Step 9 - Browse to the file downloaded in Step 6 and press on ok button

Step 9 - You will observe that all the fields will be auto populated. Now, click on Publish button

Step 10 - After some time you will see a success message and status as Publish succeed

Step 11 - Now navigate back to your azure web app and click on browse button

Your Website is Published

Happy Coding 😊