Riemann (curvature ) tensor, what's the quickest way?

I am writing an exam tomorrow, i am sure i will be asked to find the curvature tensor for a given metric. I have no problem finding the non-zero christoffel symbols, but then getting the curvature tensor seems to take forever! What are the "tricks of the trade" to get the tensor quickly? Is it merely by using it's symmetries ?

Should i only plug in the non-zero christoffel symbols and then check all variations? As usual with my long distance ( crappy ) education, i have not seen an example of how it's done, ever, so i guess with most things! Then finding the curvature scalar !