How do you account for the money new business owner puts into the business to supply it initial capital?

money put in is not deductible.  it depends on what it was spent on.  start-up expenses may be deductible if the business opened in 2022 and the rule of IRC  Sec195 is met.   you have to choose an accounting method. most small businesses use the cash method of accounting see IRS https://www.irs.gov/pub/irs-pdf/p538.pdf . operating expenses after opening are deductible in the year paid. capital expenses can be depreciated but there are rule special rules for "small" expenditures for things like equipment and computers.

** you should visit this IRS website for small businesses or consult a pro for the first year. mess up and the problems can cause enormous pain in the pocketbook later.  

https://www.irs.gov/businesses/small-businesses-self-employed