Rule of thumb for herbs is: use roughly 2-3 times as much fresh herb as dried herb. ie is your recipe calls for 1 tablespoon dried basil, then use 2-3 tablespoons fresh basil. It doesn't need to be precise! A good sized sprig will do the trick. Best to add fresh herbs towards the end of cooking time, too. Some lose their flavour with prolonged cooking, others become bitter. It's trial and error. Basil is very well-behaved, and retains its flavour well.
And definitely, fresh really IS best when it comes to the majority of herbs. You can be surprised at the difference in flavour. To me, dried basil tastes not unlike dried grass.