The key thing about sailing deep downwind - ie on training runs or runs, is that you need to be just as aware of changes in wind (or your) direction as when you are beating, but its a lot less obvious when it happens.
Topper Topaz Race sailing downwind, goose wing sails and daggerboard up. Island Barn Reservoir Sailing Club.
When you are sailing on a beat or a reach the air is flowing smoothly across the sail, in the same way that it does across an aeroplane wing. Its obvious if the sail is let out too far - the front of the sail flaps, and its reasonably obvious if the sail is pulled in too far - the boat feels all sluggish and unhappy. You may not have noticed this yet, but you soon will.
But when you are running the wind isn't flowing across the sail. Its coming from behind and hitting the sail, pushing you along by brute force. You just don't have the same sort of clues with how the boat feels, so you have got to be more consciously alert. What you particularly need to be aware of is accidental gybes. Gybing deliberately is no great problem (we'll come to that next week), but an accidental gybe can leave you and the sail on the same side of the boat, perhaps shortly to be the underwater side! So keep an eye on your wind indicator, and make sure that the wind is coming from your side of the boat.
To go faster downwind you can lift the centreboard (or daggerboard) a lot. There is little or no side force from the sails so you don't need much centreboard - having it right down adds more drag to the boat. In light weather you can easy the kicking strap to allow the top of the sail to twist a bit more. This is most important in boats with shrouds (side stays on the mast) which stop the boom and lower part of the sail going right out. In a laser or topper with an unstayed mast it is less important because you can let the boom right out to 90 degrees.