There are a ton of ways to track performance of a website or marketing campaign. And often the tools depend on the specific situation. You can easily use one of a half-dozen different software packages, each with various pro's and con's.
Here are a few options that I've found are helpful regardless of the situation, or are great for people just getting started in the world of website and marketing optimization.
For website and marketing analytics, Google Analytics is the defacto standard for tracking website performance. Use it, know it, love it.
Unbounce or Click Funnels are popular for marketing and landing page optimization, but since I like building my sites in WordPress, I often use Nelio for A/B testing, combined with Crazy Egg for heatmap and clickmap analysis.
There are a lot of email marketing programs, but I really like what ConvertKit is doing and recommend it has a good place to start. Infusionsoft is popular but a bit of a beast.