How do I file taxes with my husband if he quit his regular job in August of 2023 and started a sole proprietor LLC?

You will still file as married.  Typically married filing jointly yields the best tax result.  You will enter your husband's self-employed business in the "Wages & Income" section using the self-employment topic. This will generate a Schedule C for that income source.  In the self-employment topic you can also enter his business expenses so that only his net income is taxed.  

Here is a helpful link.

Be advised the social security and medicare taxes are split between the employer and employee but as a self-employed taxpayer the sole proprietor is both the employer and the employee so those taxes will be added to your return as self-employment taxes.   TurboTax will automatically calculate those and add the proper forms for reporting using your entries in the self-employment topic.

Here is a link with more information on self-employment taxes.