I was self employed during the year and didn't realize I had to make estimated payments
Sometimes a person starts a business or goes from being employed (W-2) to self-employed (1099) and doesn't realize that income taxes were not being withheld. You have an obligation, if you are not having taxes withheld for you by an employer, to make estimated tax payments. Usually this is for SCHEDULE C filers. Estimated tax payments are usually made on a quarterly basis. So practically speaking you need to be disciplined and set money aside on a regular basis so that you can make the payments. It is usually wise to have a qualified accountant (I recommend a CPA) to help with tax planning in this regard so they will give you DUE DATES and payment amounts/coupons based on your prior year income. You can pay by check or Online using the IRS' EFTPS system. These requirements also apply to state income taxes.
So, anyway, I have a balance due and cannot pay it in full
So, let's say that no matter how you got there, you complete your tax return(s) and have a balance due. What do you do? First, do not panic. You are not the first person, nor the last, to have a tax bill. If the bill is high and you don't think it is correct after doing it on TurboTax perhaps its time to use a professional? CPAs and many experienced tax preparers know things you do not about when and how to take deductions or take advantage of credits. You can submit your return with a request for installment agreement (IRS Form 9465) where you note the balance due and the amount you propose to pay. In most cases, and depending on the balance, if you propose a payment plan that will pay the liability off in 48 to 60 months or less you will be okay. Submit it with the first payment and the user fee. You can also call the IRS and ask them for assistance. Most IRS representatives are pretty friendly and will walk you through it.
What if I have a large balance or owe for multiple years?
If you have a large balance due (say over 10,000 or even 25,000) it is probably time to enlist professional help unless you can full pay or full pay in a relatively short period of time. Keep in mind that if you don't full pay and the balances get to this point it is very likely the IRS will file a Notice of Federal Tax Lien against your real estate.
What if I can't pay quickly enough?
If you can only make small monthly payments the situation becomes more complicated and you really, again, should seek professional help. When you get to this point you will need to file a financial statement indicating your sources of income, assets, and expenses to come to a monthly payment figure. If the payments you can make under IRS guidelines are legitimate but will result in taking more than 48, 60 or 72 months depending on the situation the financial statement will be scrutinized and you will likely have to provide backup information (bank statements, utility bills, income statements).
Should I get a state or federal payment plan first?
I usually advise clients to secure a payment plan on non-federal taxes first because most states have less wiggle room and are always behind the IRS in getting paid. The good news is, if you have a set state/local payment plan in place, it is a legitimate expense you can list on your federal financial statement.