Normal Summon

A Normal Summon can normally be conducted only once per turn. Setting a monster will also take up your Normal Summon for the turn.
Some cards can change the Normal Summoning rules. "Ultimate Offering", for example, allows you to pay 500 Life Points for each extra Normal Summon you wish to perform in a turn. "Double Summon" allows you to Normal Summon twice in one turn.
Only monsters that are Level 4 or lower can be Normal Summoned without Tribute (Tribute Summoning is still considered Normal Summoning, however) unless specifically designated on the card text (Example: "Swift Gaia the Fierce Knight")