Instagram has added a payments feature to its application recently that will finally allow users to make purchases from within the app and without having to be redirected to an outside website. Though not all web pages that offer e-commerce options will have this payment feature enabled yet, some some e-commerce accounts are already using it now that Instagram has laid the groundwork and turned on the feature. That said, before you can actually make any payments for anything you'll have to add a credit or debit card to your Instagram account just as you would if you were trying to use Google Pay or Samsung Pay to make a purchase.
As an added bit of security you can set up a PIN that will need to be entered before the app will let any attempted payments go through, which might be a smart move if you're worried about someone getting a hold of your phone and potentially making a bunch of crazy purchases. That said, such a scenario probably isn't very likely but it never hurts to have extra security when available. Aside from the security and profile tabs, there's also an activity tab where you can see any details for the purchases that you have already made.
If you haven't noticed the payments feature inside of Instagram you'd be forgiven for missing it, as Instagram never advertised that payments were being added and it's not exactly easy to find. The only way you'd notice is if you happened to stumble on an e-commerce account that supported it and you made a purchase, or if you entered int the settings just to poke around, which is where you'll find the options for payments hidden away. To get to the payments menu where you can set up your PIN and add the cards you'll want to use, head to your account page (the button all the way to right in the bottom nav bar), tap the overflow menu in the top right corner to get to account options, then scroll down until you get to the settings category and payments will be one of the last options under this header. Tap that and you can set everything up. It's not clear if this was a service-wide rollout or not, so if you're interested in using it you'll need to check and see if the option is there.