What can I do?
This is a simple issue that can be quickly rectified by following the steps below:
Go ahead and create a new account using whatever authentication service you were using previously. Make a note of the profile URL - you can get to the new profile by clicking on your user name at the top of the page. Keep this handy.
Locate your original ...
It seems there are two users called passerby51, one who has been a memeber for 53 days, the other has been a memeber for 2.5 years, and has 6 questions and an answer. If both of these are you, request that the two accounts be merged.
see How do I combine my two accounts?
The procedure appears to be:
1) Have third-party cookies turned off.
2) Log into MathOverflow with the desired account.
3) Clear all cookie data for all sites ending in stackexchange.com
4) Log into ***.stackexchange with the desired account.
The order very much matters.
I haven't managed to reproduce the effect you're describing.
I'm not computer-savvy either, but this is what I see when I go to MathOverflow in a window where the history doesn't show I'm already logged in (e.g., a private window). In the menu up at the top there's a Log In button, next to Sign Up. Here I'm using FireFox 60.0.2.
(If I'm already logged in ...
Right now (December 2018), the answer is: there is a striped "speech balloon" icon on the top right of the page, and clicking it will reveal a menu with a "log out" link.
I imagine the answer to this question may continue to change over time, as Stack Exchange continues to redesign the user interface. The current answer can be found at this page: How to ...
You can just use the "click here to recover your account" link on the login page. You should then receive an email with a link to a form to set a new password. Afterwards you should be able to log in by choosing "log in with Stack Exchange".