Website Optimization Tools
Most of the major search engines (Yahoo!, Bing and Google) provide free tools for Webmasters to monitor the performance of their Website that was crawled and indexed by the search engine. These tools provide Webmasters with detailed information about their Website's visibility on the search engine. These tools can help identify and diagnose problems, discover link and query traffic and be used as a portal to share information about the Website (with the search engine).
Google's Search Console
Google Search Console provides Webmasters with detailed information about their Website's visibility on Google. It helps identify and diagnose problems, discover link and query traffic and share information about the Website.
Adding a site (to Google Search Console)
The following two Webmaster Help Articles cover the options for adding and verifying a Website on Google Search Console:
 “Adding a Site (to a Webmaster Tools account)” Google Search Console Help Article
 “Choose a verification method” Google Search Console Help Article
Website Analytics Packages
Web analytics is the measurement, collection, analysis and reporting of internet data for purposes of understanding and optimizing web usage. Web analytics is not just a tool for measuring website traffic, but it can be used as a tool for business and market research.
It can estimate how the website traffic changed after the launch of a new advertising campaign. Web analytics provides data on the number of visitors, page views, etc. to gauge the traffic and popularity trends which helps doing the market research.
Google Analytics is an enterprise-class web analytics solution that gives you rich insights into website traffic and marketing effectiveness. To get started, click on the "Sign Up Now" link on the right side of the screen: Google Analytics