If I received unemployment last year 2019, do I have to file it on my 2019 tax return or wait until 2020 tax return?

Unemployment compensation you received in 2019 needs to be entered on your 2019 tax return.  You cannot wait and put 2019 income on your 2020 tax return.  If you did not include the unemployment on the 2019 return you filed then AFTER it has been fully processed you need to amend the 2019 return.  You should have a 1099G from the state--you might need to go on the state's unemployment web site to get your 2019 1099G.

If you are receiving unemployment during 2020 that will go on your 2020 return when you prepare and file your 2020 return in early 2021.  Again--you will get a 2020 1099G that must be entered.

To enter unemployment income--go to Federal>Wages and Income>Unemployment.

Be aware that unemployment compensation is taxable income on your federal return and on some state tax returns.  To avoid a nasty tax bill next year, it is a good idea to have federal (and maybe state) tax withheld from your unemployment.

To amend your 2019 return:

How do I amend my 2019 TurboTax Online return?

STATES THAT TAX UNEMPLOYMENT BENEFITS

AZ, AR, CO, CT, DE, DC, GA, HI, ID, IL, IN, IA, KS, KY, LA, MA, ME, MD, MI, MN, MS, MO, NB, NM, NY,NC, ND, OH, OK, OR, RI, SC, UT, VT, WV, WI