Creating a custom Master page in SharePoint 2010 using Visual Studio 2010

Lets create a custom master page in SharePoint 2010 using Visual Studio 2010.
Steps Involved:

• Open Visual Studio 2010.
• Go to File => New => Project.
• Select Empty SharePoint Project from the installed template SharePoint 2010.
  
   
• Enter the Name.
• Click Ok.
• Enter the local site that you want to use it for debugging.
• Select "Deploy as a sandbox solution".
• Click Finish.
• Right click on the solution and click on "Add a new item".
• Select the Module template from the installed templates.
  
   
• Enter the name and click ok.
• Rename the Sample.txt to Sample.master.
• Replace the code with the following code snippet.
  
  <?xml version="1.0" encoding="utf-8"?>
  <Elements xmlns="http://schemas.microsoft.com/sharepoint/">
    <Module Name="Module" List="116" Url="_catalogs/masterpage">
      <File Path="Module\Sample.master" Url="Module/Sample.master" Type="GhostableInLibrary" IgnoreIfAlreadyExists="false" />
    </Module>
  </Elements>
   
• Go to the SharePoint Designer.
• Open some existing site in the SharePoint Designer 2010.
• Go to Navigation => Site Objects =>Master Pages.
• Make a copy of v4.master.
• Do some modifications in the copy of v4.master and copy the code.
• Paste the code in the Sample.master.

Publish the master page:

• Go to Site Actions => Site Settings =>Galleries => Master pages and page layouts => Module =>Sample.master.
• Go to the ECB menu, click on "Check in". 
• Go to the ECB menu, click on "Publish a major version".  
• Go to the ECB menu, click on "Approve/Reject".  
• Select the "Approved" option. Click on Ok

Change the master page of the SharePoint site with the custom master page

• Go to the SharePoint Site => Site Actions => Site Settings => Site Collection Administration => Site Collection Features.
• Activate the following feature "SharePoint Server Publishing Infrastructure".  
• Go to Site Actions => Site Settings =>Site Actions => Manage Site Features.
• Activate the following feature "SharePoint Server Publishing".  
• Go to Site Actions => Site Settings => Look and feel => Master Page.
• Select the custom master page as shown in the following.
  
• Click Ok.

Refer: c-sharpcorner