First, wait until your current billing cycle finishes. SE supposedly adjusts/pro-rates if you change an option mid-cycle, but I haven't tested this myself.
Log into SE's site  or Mog Station.
Click "Account Services" up near the top.
Click "Reoccurring Subscription Setup" on the Final Fantasy XIV tab.
Scroll down to your billing information, first option is your subscription type. Click from "Entry" to "Standard".
From there, you do need to continue through your billing information. You're basically just confirming that the rest of your information is still correct at this point. If you back out/close/cancel before you finish going through this information, your account won't be changed from Entry to Standard.
Log into SE's site  or Mog Station.
Click "Account Services" up near the top.
Click "Reoccurring Subscription Setup" on the Final Fantasy XIV tab.
Scroll down to your billing information, first option is your subscription type. Click from "Entry" to "Standard".
From there, you do need to continue through your billing information. You're basically just confirming that the rest of your information is still correct at this point. If you back out/close/cancel before you finish going through this information, your account won't be changed from Entry to Standard.