Are you talking from experience here, or in the event of? If the latter your developer shouldn't have access to be able to
DROP a production database; they are developers after all. After that problem is solved then the issue can't happen.
If the former, the first thing you need to do is get your system back up and running. You'll need to restore the latest backup of your database, which if you are using transaction logs hopefully won't be too old. After that ensure you have documented how much potential data you have lost; for example if you perform a transaction log backup every 10 minutes and the
DROP occurred at 19:05 then you probably had 5 minutes of lost data. What you do about that is up to the business, as we have no exposure to the information you're working with. If you have logs that record the actions taken on the application else where, then it's time to start trawling through those to try and recover as much data as possible.
Then, finally, you need to see my initial point; revoke the permissions of your developers, they should not be able to
DROP a production database. It's then up the the business to decide if any re-training, disciplinary action is taken against the developer, DBA, responsible persons (in my view, the developer is not solely at fault).
Excuse my typos and sometimes awful grammar. My fingers work faster than my brain does.