Have you already registered at https://marketingplatform.google.com/intl/de/about/analytics/? Because this is your first step. With a Google Analytics account you can then use most of the offered tools for free. Just save the URL of your online shop (your URL is the adress you find in the URL-window when publishing your shop) and you are able to let your shop be tracked. Like this you get to know e.g. how many people visit your shop, how old they are, where they are from, how they found your online shop and what's their favourite time to make purchases in your shop. You can use this data as well as the
information to purchase cancellations or the devices your online costumers are using to find out where your strenghts and weaknesses are and what you can improve in the near future.

In addition to that you can use the campaign tool to pay for certain keywords with which you expect your online shop to be found. In return you will receive a better ranking for these keywords through google search.
Marketingwise the connection to Google Analytics is an enrichment in any way which is why should really consider using it.