How is a conversion different from a transfer?
Moving between traditional IRA custodians ordinarily preserves the account's tax treatment. Moving traditional IRA assets to a Roth changes it. Even a direct trustee-to-trustee movement can be a taxable conversion. IRS Publication 590-A describes the permitted conversion methods and income treatment.
How is the taxable amount determined?
It depends on the assets converted and applicable IRA basis rules. Do not assume you can select only after-tax dollars while ignoring other relevant IRA balances. Coordinate the calculation and reporting with your tax adviser and custodian before instructing the move.
How does a Roth conversion show up in practice?
Hypothetically, converting $20,000 from an entirely pre-tax traditional IRA, with no after-tax basis in the relevant IRAs, generally adds $20,000 to taxable income. That is the income amount, not the tax bill. The actual tax depends on the taxpayer's circumstances.