I completed a one-time technical writing project which paid me $250. I don't plan on doing more contract work this year and was wondering how I need to report and pay taxes for this income? Do I need to submit a quarterly statement or can I just added to next years income taxes? I believe they will provide me with a 1099 statement.
or can I just added to next years income taxes?
Of course, it goes on this year's income taxes, but that's probably what you meant.
Since it's so late in the year, and just $250, I'd just add it to your 2019 Tax Return and call it a day.
(I hope you put about $50 away for the taxes you might owe on it.)
I believe they will provide me with a 1099 statement.
Income from contract work is considered business income and gets entered via Schedule C (or C-EZ) regardless of whether or not that income is reported to the IRS separately via 1099. You'll also record any appropriate expenses that might offset this income. If after factoring in expenses there's more than $400 of profit from all self-employment activities then you carry forward that amount to Schedule SE to calculate self-employment tax due. Since the amount in this case is under $400 there is no need for Schedule SE and you will pay no self-employment tax.
Do I need to submit a quarterly statement or can I just added to next years income taxes?
With $250 of income this is not an issue unless you had other significant changes to your income for the year, so just wait until you file this year's income tax return next year.