Using the clowns and putting defensive spell/trap cards, the clowns will have decent survivability, and will be able to destroy your opponent's monster easily. This can open up your opponent to some direct attacks. Using the skill to summon Barrel Dragon at the right time can let you end the duel early.
What you summon early in the duel mostly depends on what you get in your starting hand, but there are some things to consider before choosing which one to summon. 4-Starred Ladybug of Doom can be a safe option if you get first turn, while Barrel Dragon and Sergeant Electro are for when you want to use their effects. In most cases, getting some defensive spell/trap cards is good for Dream Clown so you can destroy your opponent's monster. Follow it up with Sergeant to start locking your opponent's spell/trap cards, then Barrel Dragon to finish the duel.
With only 1 Supremacy Berry in the deck, you can only use the skill once or twice. Instead of summoning early, it's recommended to either wait until you get Berry in your hand, or when you can finish off your opponent. You will also have to pay attention to the matchup. If you see your opponent using normal monsters, it can mean they might have an Order to Charge, or a Champion's Vigilance when going against a 3 star demotion decks and a high level dragon deck. Use the skill cautiously and summon early to prevent a Vigilance, while using it later to avoid a Order to Charge.