Driving from Tallinn is fairly simple. Just head out of town on Tartu mnt. and once you get past the airport, it's a straight shot all the way down. Once you reach Tartu, there are a couple of twists and turns you'll have to make to get into the centre, so we recommend you glance at a map and pay attention to the signs before arriving.
Those driving from Latvia should be aware that, though there are no checks at the border, border guards sometimes stop vehicles a few kilometres into Estonia to check documents.