If I take an early withdrawal from my 401k, how will I be penalized come tax season?

You will pay (a) federal income tax, (b) state/local incoime tax (as appropriate for where you live), and (c) an early withdrawal penalty of 10%.

If you need cash from your 401(k) and are still employed at the same company where your 401(k) is located, consider taking a loan from yhour account rather than a withdrawal - there are no taxes nor early withdrawal penalty when you take a loan. Of course, you have to be able to pay the loan back over time.