Basically there several LTCG rates (e.g. 0%, 15%, 20%) each of which applies to certain brackets of income. Using round numbers for singles in 2019, %0 for $0 to $40k, 15% from $40k to $440k, 20% over that. (plus possible net investment income tax for higher earners but that isn't applies to all income not just capital gains.)
Ordinary income fills up these brackets first and is taxed at regular income rates. LTCG then fills up the remaining and is taxed at the special rates.
Again, simplifying, if you had $30k of ordinary income and $100k of capital gains you would pay ordinary rates on $30k, 0% on $10k and 15% on $90k.
If you had $60k of ordinary income and $100k of LTCG it would be ordinary rates for $60k plus 15% of $100k
See the worksheet on Schedule D (instructions at page D-16) for the super complicated calculation. https://www.irs.gov/pub/irs-pdf/i1040sd.pdf
See this for a general description: https://www.nerdwallet.com/blog/taxes/capital-gains-tax-rates/
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