Your cost basis in a gift is usually the same as the givers basis. For example, if your father gives you 100 shares of XYZ corporation that your father purchased for $3,000 10 years ago, then your cost basis will be the same as your father's and will be $3,000 and your date acquired will be the same as your father's and will be the date 10 years ago that your father purchased the stocks.
If you receive a gift of property that has lost some of its original value, such as your father gives you stock that he purchased for $3,000 10 years ago, but now the stock is only worth $1,000, then the rules get more complicated. In this scenario, your cost basis for calculating gain is the original value, but your cost basis for calculating a loss is the fair market value of the stock on the date you received the gift. For example, if you sell the stock your father gave you 4 years after receiving it as a gift for $4,000 then your cost basis would be $3,000 and you would report a gain of $1,000. If you sold the stock immediately after receiving it for $1,000, then your cost basis would be $1,000 and you would report $0 gain or loss.