How do I calculate how much taxes i will owe at the end of the year if my new employer is not with holding taxes from my weekly pay check?

Are they paying you as an Independent Contractor on a 1099?  They don't take out Social Security or Medicare either?  You better double check with them.  

But if  they are paying you as self employed you have to pay Self Employment tax.    Self Employment tax (Scheduled SE) is automatically generated if a person has $400 or more of net profit from self-employment. You pay 15.3% SE tax on 92.35% of your Net Profit (If it is greater than $400). The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare (FICA). So you get social security credit for it when you retire.  The SE Tax is in addition to the regular income tax on your profit.  

If you are self employed I can give you more info and links on how to prepare for it and report it.  

You must make quarterly estimated tax payments for the current tax year if both of the following apply:
- 1. You expect to owe at least $1,000 in tax for the current tax year, after subtracting your withholding and credits.

- 2. You expect your withholding and credits to be less than the smaller of:
90% of the tax to be shown on your current year’s tax return, or
100% of the tax shown on your prior year’s tax return. (Your prior year tax return must cover all 12 months.)

The 1040ES quarterly estimates are due April 18, June 15, Sept 15 and Jan 16, 2024. Your state will also have their own estimate forms.

How to make the Estimated payments
https://ttlc.intuit.com/community/tax-payments/help/how-do-i-make-estimated-tax-payments/00/25875

Here are the blank Estimates and instructions…..
https://www.irs.gov/pub/irs-pdf/f1040es.pdf

Or you can pay on the IRS website. Be sure to pick 2023 1040ES payment
https://www.irs.gov/payments

Are you going to receive a W-2 from the employer?  Or are you working as an independent contractor?   Is any Social Security or Medicare being withheld from your paychecks?  Better find out now why no tax is being withheld.    If you are working as an independent contractor then you are going to have to pay self-employment tax for Social Security and Medicare as well as ordinary income tax.    You need to understand what kind of tax document you will be getting in January.   If you are really an employee then you can fill out a W-4 and give it to the employer so they will withhold tax.   If you are an independent contractor then it is all up to you to plan, save and expect to pay at tax time.

https://ttlc.intuit.com/questions/2584365-am-i-an-employee-or-an-independent-contractor

https://ttlc.intuit.com/turbotax-support/en-us/help-article/form-1099-nec/1099-nec/L5qTsBiSe_US_en_US

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c

https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct

https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs

https://turbotax.intuit.com/tax-tools/calculators/self-employed/

https://www.irs.gov/individuals/tax-withholding-estimator

https://www.irs.gov/pub/irs-pdf/fw4.pdf