Hey there AffinityGadgets
Congratulations on your first sale! That is awesome to hear.
No worries about being confused. This happened to me the first time too, I thought I was going to rip my hair out in frustration! Once you learn it once though, you will be good to go!
From your information, it sounds like you are missing the free Oberlo Google Chrome Extension. You need this to see that orange order products button!
Then, you can press it and it will take you to Aliexpress to pay the supplier. Here is a guide on how to do so as well. Let me know how that goes, or if you come across any hiccups. We can go from there to make sure your order is properly processed.