Yes, to determine your cost basis multiply the number of shares that were issued to you by the stock price on the day they were issued and the resulting number will be your total cost basis. You can use the same method to calculate the total sale proceeds too. That is, multiply the shares you sold by the stock's sale price. If you paid commissions/fees when selling, add those commissions/fees to your cost basis. You don't need to pay tax on commissions/fees, therefore add that amount, if any, to your cost basis so that your sales proceeds reflect the correct gain or loss.
Sometimes taxpayers will ask what price they should use when calculating cost basis. For example, should they use the price at market open, or the price when the market closed, or should they use the average price on the day the shares vested. That determination must be made by the taxpayer in consultation with their employer. The employer's plan will probably include information about what price was used when the employer sold shares to cover tax withholding, and that is probably the price the employee/taxpayer should use when determining their cost basis.
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