I've noticed a few people are having trouble with pendulum summons so I decided to do this lesson.
First off lets start with the new pendulum zones. This is where you place the pendulum monsters. While in this zone they count as a Spell card and gain the Top effect only. An example of this is Odd-Eyes Pendulum Dragon. Here is the effect he gains while in the Pendulum Zone: You take no battle damage from attacks involving a Pendulum Monster you control. During your End Phase: You can destroy this card, and if you do, add 1 Pendulum Monster with 1500 or less ATK from your Deck to your hand. If you use this effect you do not send Odd-eyes to the grave as you normally would any other card but instead he goes to the Extra Deck Faceup for others to see. Also while in this zone they can be hit with Mystical Space Typhoon.
Next up are the Pendulum Scales. These are found beside the First effect of the Pendulum Monster. Example Stargazer Magician has a scale of 1 while Timegazer Magician has a scale of 12 . This means you can only Pendulum Summon Monsters thats level are 2-11. You cannot Pendulum Summon a level 1 or 12 since the Scale starts with 1 and ends with 12.
Now lets go into Pendulum Summoning. If you have say for example Stargazer Magician and Time gazer Magician in your pendulum Zones you can preform a pendulum summon. This is done only once per turn and you have to declare you are going to Pendulum summon. When Declared you can summon as many monsters from hand and Pendulum monsters that are faceup in your Extra Deck.
Your opponent can activate Slemn Warning in response to this summon.
Hope this helps a little since pendulums are still new to us and more will be explained as more is revealed about them.
Remember Hand control is everything with this new card type and be careful you don't kill yourself by going full out during your pendulum summons.