Multiply each possible value of the variable by the probability of it occurring and add all these values together to find the mean of the discrete random variable. For example, if a wallet contains $1, $5 and $20 bills and the probabilities of pulling one of them out of the wallet are 0.5, 0.4 and 0.1, respectively, the mean is 0.5*$1 + 0.4*$5 + 0.1*$20 = $4.50.
Subtract the mean value from the first possible value, square the result, then multiply by the probability of that value occurring. For the $1 bills, for example, [($1 - $4.50)^2]*0.5 = $6.125. Repeat the procedure for all the other possible values; in this case, [($5 - $4.50)^2]*0.4 = $0.10 and [($20 - $4.50)^2]*0.1 = $24.025.
Sum all the values you calculated to find the variance of the discrete probability distribution. For example, the variance of $1, $5 and $20 bills with probabilities of 0.5, 0.4 and 0.1 is $6.135 + $0.10 + $24.025 = $30.26.