You don't report rollover unless you have the form 1099-R. I recommend contacting your broker/administrator to verify if the Form 1099-R will be issued. 

However, if the direct rollover was made as a trustee-to-trustee transfer involving no payment or distribution to you, you should not be receiving Form 1099-R and there is nothing to report on your tax return. 

A direct rollover, which is the direct payment to you of an eligible rollover distribution to a traditional IRA or other eligible tax-qualified plan, is reported on Form 1099-R, which you should report in the retirement income section. You will be able to report the form and answer the following questions indicating rollover, which will result as a nontaxable transaction. 

I  left a job in January 2020. One month later, I withdrew my total IRA account balance as a direct payment to me with 20% federal income tax withholding. The payment is considered an eligible rollover distrubution. I expected it to take a few months for me to receive the payment check, but it was mailed the day after I filed my federal 1040 so I received it one week after I filed federal 1040. Since 20% was already deducted from my payment, I don't know if I need to report it to the IRS and if it should go on my 2019 or my 2020 income tax form. I haven't received a 1099-R form yet if one is to be expected? IF it needs to go on my 2019 income tax form, I don't know which forms to submit to amend it. Would I need to add this as income since it was already taxed with 20% withholding?

A regular distribution that occurred in 2020 goes on your 2020 tax return, not your 2019 tax return, and generally has no effect on your 2019 tax return.  However, if you do not roll over the entire gross amount, it could affect the amount of Retirement Savings Contributions Credit you (or your spouse) might otherwise be eligible to receive on your 2019 tax return and would have to be included on 2019 Form 8880.

By rolling over, do you mean transferring it to another IRA account instead of withdrawing the total amount in payment directly to me? My 2019 tax return showed a low income savers credit of $150 for my IRA (same as Retirement Savings Contributions Credit?). Again, I filed my 2019 taxes before I received the check. Do I need to fill out form 8880 for 2019 or 2020?

Since the distribution was paid to you personally, a rollover of the entire gross amount would require that within 60 days of receipt of the distribution you deposit the money into another qualified retirement account like an IRA.

Yes, "Savers Credit" is a common nickname for the Retirement Savings Contribution Credit calculated on Form 8880.  If you do not roll your recent distribution over, you'll have to file an amended tax return (Form 1040-X) along with an amended 2019 Form 8880 to account for this distribution reducing the amount of the credit originally calculated on this form (assuming that you did not already include this distribution on line 4 of this form), and pay the balance due.  It may end up being that the entire credit is disallowed and you'll have a balance due of $150 with your amendment.  (This is an anti-abuse provision to prevent you from taking money out of a retirement account just to put it back in just to get the credit without actually increasing your retirement savings.  This applies even if you take the money out after filing but before the due date of your tax return, as you did in this case.)

Be aware that you are only allowed one rollover in a 365-day period (actually 366 days since this is a leap-year).

Although I didn't receive a 1099-R in the mail, I need to amend my 2019 taxes or not wait until I receive a 1099-R in the mail to include it in 2020 instead of 2019 taxes? I was confused by somethng I read about receiving the distribution in the past 12 months. When I file my 2020 taxes, the payment would be in the past 12 months. I took the money out because it was less than $1000 or wouldn't earn much interest over time because further contributions can't be made to it unless you're still employed there. I don't know much about IRAs, but 20% would still be withheld if I trannsferred it to another IRA? I don't know how to find another IRA, but I think I'll just keep the money.

First, because 20% was withheld for taxes, I suspect that the employer plan was a qualified retirement plan like a 401(k), not and IRA.  You'll want to be clear on the type of plan that the employer had because unlike IRA-to-IRA rollovers there are no limitations on how frequently you can do a rollovers from a qualified retirement plan.

This distribution in 2020 likely disqualifies you for some of the credit that you received on your 2019 tax return, so yes, you need to amend your 2019 tax return.

The 20% has already been withheld and that will be credited to you on your 2020 tax return.  To be able to roll that 20% over by the 60-day deadline you'll have to substitute other funds.

If you are under age 59½, just keeping the money will subject the entire amount, including the 20% withheld for taxes, to ordinary income tax plus a 10% early-distribution penalty on your 2020 tax return in addition to probably eliminating the $150 credit on your 2019 tax return.  Losing that much money by not rolling over the funds is generally not the best financial decision.

I am under 59. It must be a 401k or it is government thrift savings plan. I thought since I had savings ir was saving in 2019, it would not apply to my 2019 taxes. It is 2020 when I withdrew the money. It had 3% interest which isn't much on $700, and they said I could no longer and they would no longer add contributions to it after I left the company. 

---

@matt666666 wrote:

I am under 59. It must be a 401k or it is government thrift savings plan. I thought since I had savings ir was saving in 2019, it would not apply to my 2019 taxes. It is 2020 when I withdrew the money. It had 3% interest which isn't much on $700, and they said I could no longer and they would no longer add contributions to it after I left the company. 

---

If you received a distribution from a tax deferred retirement account in 2020 you will receive a Form 1099-R in January 2021 reporting the distribution.  You enter the Form 1099-R on your 2020 tax return next year.

It makes more sense to report what I received this year next year. So, I still keep the $150 Saver's Credit then?