Federal - you get the option to withhold 10% for federal taxes on unemployment. If you didn't do that, then yeah, this is gonna get pretty bad. This is an example calculation for a single person. If you were on NY unemployment for 9 months, getting the max, you might have gotten up to 30,000 of unemployment. Adding in what you might have earned in the 10 weeks we had before everything went to h*ll, your overall tax rate would be in the range of 7 to 8%. So the 10% would cover you just fine, and you will likely get a refund. If you didn't withhold, plan to have to pay 7 to 8% on however much unemployment you got.
Will the 10% definitely be enough to cover you? Yes, unless your overall income rises over 45k, then your tax rate will be higher than 10% so the withholding won't be enough to cover it and you might owe unless you have enough coverage from your other income.
States - different states handle this very differently. NY and NYC tax unemployment like regular income. NY only withholds 2.5% and it is pretty much never enough, especially not for NYC taxes as well. Unless your income is really low, under 13k, it's not going to be enough for a NYC resident. So if you are a NYC resident who was on unemployment, plan to have to pay state. If you are a NYer outside of NYC or not a resident of NY, but you got NY unemployment, you still have to pay taxes in NY, but at least it's not NYC. But again, the 2.5% will not be enough if your income is over 20,000. NY taxes ramp up pretty fast unfortunately.
What about other states? Well if you live in a state with no income tax, they won't tax your unemployment of course. And CA, MT, NJ, OR, PA, and VA do not tax unemployment, so yay! IL charges, but they have a flat tax, so the withholding should be close. And that covers most of my clients, if there is another state you want me to look into, let me know.
What if you live in one state, but got unemployment in another? Well, it's just like having a job in another state, you have to pay in the state that gave you the unemployment and take a credit in your home state, if applicable. So if you are, for example, a resident of NJ who got NY unemployment, then you have to pay NY. NJ won't charge you, but you still have to pay NY. Of course. If you are, say, a CT resident who got NY unemployment, CT taxes are lower and so while you might have to pay NY, you will get a credit for paying them in CT and that should cover you. Be warned, if you are a NY resident, but got unemployment from say, NJ or CA that don't tax unemployment and therefore don't withhold, you are screwed and will have to pay NY (and NYC if you live there too). If you are a resident of NY/NYC and you got unemployment from, say, CT, where they do withhold but not enough, you will also have to pay the difference. Basically living in NY/NYC is going to force you to pay. Start preparing now! Also be warned, MD doesn't charge taxes to non-residents for unemployment, so they often don't do state withholding, so if you got MD unemployment but live in a state that does tax unemployment, you are going to have to pay.
Bottom line, most people should be ok on the federal but there are a LOT of scenarios where you might owe quite a bit to states, so be prepared! File as early as you can so you have as much time as possible before taxes are due April 15.