After converting traditional IRA to Roth IRA and selecting 0 dollar tax withheld, how and when to pay tax using saving's money to avoid penalty at tax filing season?

I recommend calculating the estimated taxes based on your last year's marginal tax rate (highest tax rate calculated) and making the estimated tax payment via IRS Direct Pay: https://www.irs.gov/payments/direct-pay

Depending on your state, you may or may not want to make a state estimated tax payment.