Instructions
Acquire Tuner cards. These are randomly found in Booster Packs, which you get by fighting duelists in Story Mode. Speak with as many non-playable characters (NPCs) as you can while you are walking around the city to start duels. Synchro Monsters can also be obtained by fighting in duels.
Check the level of your Synchro Monster. When tributing cards to summon Synchro Monsters, the total level of the tributed cards must be equal to the level of the Synchro Monster. For example, if you have a level 9 Synchro Monster, you must tribute a Tuner Card and at least one non-tuner card -- any monster -- whose combined level equals 9.
Play your Tuner card and another monster card during a duel any time after you have drawn the Synchro Monster card. When they are on the field, the phrase "Activate" will appear on the Synchro Monster card. Tribute the Tuner card and any additional monster cards as you would when summoning any other creature. Your Synchro Monster will move to the field.