How do I figure out the cost basis of shares I've owned for years or inherited?

Cost basis is what you originally paid plus reinvested dividends and any commissions, and it determines your taxable gain when you sell. For shares bought in 2011 or later, brokers are required to track and report "covered" basis to you and the IRS on Form 1099-B. For older "noncovered" shares you may have to reconstruct it from old statements or confirmation slips – worth the effort, because if you can't prove basis the IRS can treat it as zero, taxing the entire sale price. Inherited shares are easier: they get a stepped-up basis equal to the value on the date of death, erasing prior gains. Gifted shares carry over the giver's original basis. When you have multiple lots, use specific-identification to sell the highest-basis shares first and shrink your gain.