You'll deal with this on SCH C as a part of your 1040 personal tax return. Begin under the Business tab in the Business Income & Expenses (SCH C) section and work it through. Your purchase price will be dealt with in the Business Assets section. Any physical assets included with your purchase are entered there and will be depreciated over time. For the most part, business assets are depreciated over 39 years. But there are some types/classes of business assets that depreciate faster over a shorter period of time.
Non-physical assets you paid for, such as good will or customer lists for example are not capitalized and depreciated over time. Instead, they are amortized and deducted over time - generally the deduction for an amortized asset is spread out over 15 years, and if you have the business income in the first year, you can deduct a maximum of $5K for your amortized assets in that first year if certain specific criteria are met and satisfied.
So physical assets that you paid for are capitalized and depreciated over time, while "some" non-physical things you paid for are amortized and deducted over time.
