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Any monster of level 5 or higher requires a Tribute Summon (Advanced Summon in the OCG, previously Sacrifice Summon). Monsters that are Level 5 or 6 require one monster to be Tributed (called Release in OCG), while monsters of Level 7 or higher require 2 monsters to be Tributed. Some high-level monsters (such as "Moisture Creature") require 3 monsters to be Tributed in order to activate an effect.
Even if the monster is Tribute Set instead of Tribute Summoned, the correct number of Tributes must be offered. So you cannot Set a monster in order to avoid offering a Tribute.
A Tribute Summon is treated exactly as Normal Summon, except a few cards refer specifically to whether or not the card was Tribute Summoned (such as Monarch). Normally only one Tribute Summon can be conducted in the same turn (exceptions: see "Ultimate Offering" and "Double Summon"). This means you cannot Normal Summon or Set a low Level monster and then Tribute it immediately to Tribute Summon a high Level monster.
Tributing a monster for a Tribute Summon is not considered a cost. However, similar to paying costs, players cannot respond immediately to the Tribute of a monster, since Tributing does not have a Spell Speed. If the Tribute Summon of the new monster is negated, however, the Tributed monster will not return to the field.