If taxes aren't charging, then you'll want to confirm that you have tax rates set up for the states your customers are purchasing from. Taxes can be edited by going to Settings/Taxes. Keep in mind that you'll want to determine if you need to charge taxes for out-of-state customers. If you don't, then you wouldn't need to add additional tax rates to your admin. More information on taxes in the United States can be found here.
If you've set up tax rates for other states, and they aren't charging correctly, then I would recommend contacting Shopify Support so we can take a closer look at your account. You can do this by logging into your store through the help center, searching your question/issue, then selecting "continue" at the bottom of the page that displays the search results.
Trevor | Community Moderator @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog