The cost basis of stock you received as a gift ("gifted stock") is determined by the giver's original cost basis (what they paid for it) and the fair market value (FMV) of the stock at the time you received the gift. If it's not possible to determine what was paid for it or the date it was purchased, the FMV at the time you received the gift may be the best estimate to use as the basis.
See this help article for more information from TurboTax on determining the basis of gifted stock.
See this help article for more information from TurboTax on determining the original purchase price. For example, view the historical section at Marketwatch or Nasdaq, or Yahoo Finance as mentioned by Bees above.
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