Many a day?

[belly_ttt]

Many a day finds me locked in my room, studying
or
Many a day find me locked in my room, studying

[ptetpe]

http://www.oup.com/oald-bin/web_getald7index1a.pl

3 many a (formal) used with a singular noun and verb to mean ‘a large number of’:
Many a good man has been destroyed by drink.

[jackolantern]

I am not a teacher, but I am a native speaker.

"Many a day" is somewhat of an old phrase. The vast majority of native English speakers do not use it anymore, and it sounds kind of odd. However, it would be: "Many a day find me locked in my room studying".

A native speaker would be much more likely to say it: "Most days find me locked in my room studying." But the other way is correct English. It is just much less common.

[bhaisahab]

Many a day finds me locked in my room, studying
or
Many a day find me locked in my room, studying

Many a day finds me....

Many a day = third person singular in this sentence.

[konungursvia]

I agree with bhaisahab.