I'm not sure if there are special rules for fishermen, but in general, there are at least 2 ways to deal with this:
1) Adjust withholding at your day-job. Once your fishing income is in and known, you can make a good estimate of your taxes owed, since your teaching salary is much more predictable. So each year, you'd work up an estimate of your taxes, then taking into account anything you've already had withheld, adjust your W-4 at work to reflect that over however many paychecks are left before the end of the year. This has the benefit that the IRS treats any money withheld by your employer as having come in evenly over the course of the tax year.
2) Pay estimated tax quarterly (may be annually for fisherman - that's where a real accountant who deals with fishing income regularly could be very helpful). This may be necessary, even if you do #1 above - it is possible to have made so much money fishing, that your salary for the last few months of the year isn't enough to pay the taxes owed, once they are known.
On your fishing income, you probably owe a minimum of about 14% - that covers self-employment tax. Income, or any state taxes would be on top of that.