So we are currently using the Startup Theme.
When someone adds a product to their cart, instead of going to checkout, it just comes up with text to click on the cart or continue shopping.
How do we change this button to link to the checkout page instead?
Good theme choice. I can give you a hand with request. The start up theme is pretty awesome in the sense that it has a setting which allows you to choose what happens when you add something to your cart. Just follow the steps below and your issue will be fixed:
1) In your admin go to Online Store > Themes > and click customize theme at the top right
2) Click on the Cart Page tab on the right - https://screenshot.click/08-50-qp536-t40sy.jpg
3) Make sure to have the check turned off for "Stay on the current page when an item is added to the cart" - https://screenshot.click/08-06-ibcdv-uu7aa.jpg
That will get you sorted out! If you have any other theme specific questions you can reach out to the Startup theme developers at Pixel Union: firstname.lastname@example.org
I also suggest checking out their documentation on the Startup theme.