How can you avoid paying a large tax bill and maybe a fine at the end of the year?

You need to make sure you have paid enough taxes during the year by means of withholdings or estimated quarterly taxes so that you have at least 90% of your taxes paid. If you do not meet this threshold you will be penalized as well as having to pay the additional tax due plus interest. The actual rule to not be penalized for paying too little is that you pay in at least 90% of the total tax that you owed in the previous year. As long as you have had this much sent in to the IRS by withholding or estimated payment you won't be penalized. You could still have tax due if your income increases from year to year or if your deduction or exemptions decrease.