Basically, you just file a federal and state corporate return marked as "final" and ensure all K-1's issued are also marked "final". What other steps you may (or may not) need to take with the state depends on what type of corporation this is, be it an S-Corp or a C-Corp. You may want to seek professional help on this, as from what I read at https://www.northwestregisteredagent.com/dissolve-new-york-corporation.html it doesn't appear to me to be a simple matter of just filing a "final" corporate return.
