tribute

Let's start with: you cannot Tribute a monster for no reason - say, if all your Monster Card Zones are occupied. You cannot Tribute a monster for a Tribute Summon the turn it is Summoned, because this would violate the "1 Normal Summon or Set per turn" rule. If you have Ultimate Offering active...

The general rule is that you can only "Normal Summon or Set 1 monster per turn". Usually when people "play a monster", this is what they mean. Tribute Summons count as Normal Summons, so you cannot Normal Summon a monster and Tribute Summon in the same turn. Special Summons can be done as often...

You can Set (in face-down Defense Position) a monster that requires a Tribute by meeting the requirements to Tribute Summon the monster (i.e. tributing monster cards). If the Level 5 or higher monster would be Special Summoned by a card effect, it cannot be placed face-down unless face-down...