The first rule of taxation is you don't have to pay tax twice on the same money.
Unfortunately the first rule of Roth conversions is that you don't get to select which part of your IRA converts.
For instance if your IRA is worth $45,000 but $15,000 of that was NDIRA contribs ... and you convert $15,000... you don't get to say "we're converting the NDIRA $15,000". You must convert in proportion. Since only 1/3 of your IRA is NDIRA, 1/3 of your conversion is NDIRA, so only $5000 exempts from having to pay income tax on the conversion.
You must then remember that $10,000 of NDIRA is not yet converted. If your now-$30,000 IRA further appreciates to $40,000, and you convert $16,000, you must again say "the NDIRA portion is 25% of the IRA, so 25% of $16,000 ($4000) is exempt from income tax". That leaves $6000 of NDIRA. It's all on you to keep this paperwork straight, and have it available to present to IRS at audit.
Most people suck at keeping paperwork, so this is where it'll go off the rails for them. I keep my tax paperwork concise - forms, worksheets and W-2/1099 only, so I would write myself an explanatory letter saying what I did.
When you do a Roth conversion, that amount (minus the NDIRA exempted part) is declared as plain income on the Income section of your 1040 of the year you do the conversion. I haven't used Trump's postcard, so I'm sure it's broken into one of the numbered Schedules now. That means if you contributed to the deductible IRA while you were in a 28% bracket, and you convert while in a 0% bracket, you pay 0%. Great thing to do in a gap year! I did mine in a gap year.
What's taxable is the amount of money converted (minus the NDIRA exempted part). It doesn't really matter whether it came from initial contribution ("corpus" as we say in endowments) or appreciated value. The only part of the corpus that matters is the NDIRA part. For instance if you contribute $10,000 to a deductible IRA, and get snackered in the market and it's now worth $4000, when you convert, you pay tax on $4000.
Usually people trot out the math argument that IRAs and Roths are the same mathematically. As a math expert, I say the math doesn't address any of the "soft" issues that make Roth much more beneficial, and the last time I counted them, there were at least six. Right off the bat, no mandatory distributions. The "same mathematically" presumes uniform withdrawals from retirement to death - which is hard to do when you don't know when you're going to die, and worse, *don't know when your medical needs will flare up". I've seen people yank out $200,000 in a single year and get murdered on taxes. Not a problem on Roth.
So for all those soft reasons, I recommend Roth over IRA, and I'm happy to see you converting. However you need to plan it very carefully, so you don't accidentally create some very high tax years for yourself.
Lastly, it's always a good idea to know how to do your taxes yourself, not let TurboTax make you forget how to stick-fly an airplane. In your case, the reason is so you can grab a 1040 and a pencil and just do a "dry run" for what your taxes would look like in a variety of scenarios. Play with the numbers, see what they look like.