Hey Mick.

There are standard formulas for this and they are Var(B0_hat) = sigma^2(1/n + 1/SXX) and Var(B1_hat) = sigma^2/SXX and you can estimate sigma^2 with sigma_hat^2 which is given by sigma_hat^2 = [SYY - B1_hat^2*SXX]/(n-2).

I'm not sure what you have to do in your course, but these are some standard identities for a simple linear regression. For a multiple linear regression you can estimate the covariance matrix and use that to get all the information.