How do I move a custom field on an opportunity to the account details area?
If you want Opportunity field to be populated on Account, then you can use processs builder:
But here you will be able to see only one of opportunity data on account as you can have multiple opportunity on single account.
There certainly are ways to push information from opportunities to accounts that are easy to do, but the trouble becomes information accuracy when you potentially run into multiple opportunities all trying to push something to an account.
If you can elaborate on what type of details these are, and how you need to use them within the system from the account, then there may be better options such as showing them in the opportunity related list (if you just need to see them on an account), or using an accounts with opportunities report (if needed for reporting).
End users frequently ask for a new field that they want placed on an object to meet a reporting or other departmental business need. In many cases that field may already be available from another system where the data is trusted. It is always better to synchronize data from the trusted source and place the field on the right object. The DBA can find the right field, and help you put it on the right object. Otherwise you will inevitably run into a mismatch where no one knows which field is accurate and a clean up initiative will need to be launched.