Hmm... can anybody explain to me how XYZ or synchro works? Didn't really give a thought since those were concepts of different authors, and I only respect the original author, but then, for the sake of gameplay >.< ...
I usually use the XYZ mechanic, so I'll try to explain.
This is a pretty common XYZ monster. Instead of a Level, it has a Rank, indicated by the yellow stars coming from the left side of the card as opposed from the right. In Utopia's case, he is a Rank 4 monster that, as indicated by the "2 Level 4 Monsters" on its card, will require exactly two monsters on the field whose
levels are 4 to be placed on top of each other (overlaying) in order to be summoned. Those monsters then become XYZ Materials and can be detached from the monster to activate its effect.
On that note, other XYZ monsters might require monsters of different levels (Constellar Pleiades) or more than two monsters to be overlayed (Evilswarm Ouroboros). Also, XYZ monsters come from the Extra Deck.
Synchro Summoning is a bit more complicated.
Here's an iconic Synchro monster. As you can see, its card reads "1 Tuner + 1 or more non-tuner monsters". A tuner monster is a type of monster specifically used for synchro summoning and, like all other non-XYZ monsters, has a level. The level of the tuner and the level of the non-tuner both have to add up to exactly equal the level of the synchro monster you're trying to summon (8 in Stardust's case). You send the monsters (known as Synchro material) to the grave, and bam, Synchro monster from the extra deck.
Like with XYZ, there are other Synchros that are more complicated to pull off. Some require specific monsters or monster types to be used as a material, and others require things like 2 tuners to be used.
Learning the (sort of) new mechanics might seem a bit daunting, but its not too hard to get the hang of. Once you do though, you might find that you like it and begin to make decks centered around bringing out these kinds of monsters.