Right so, Thetia here. I'm here to explain the newest meta at the moment, pendulums. So here's how they work. I will also be using Igkights for this example, as they're really easy to use.
Right, so here goes nothing....
Okay, so
firstly) The "Pendulum Zones" Are on either side of the dueling board. Here's a pic for it; http://www.yugioh-card.com/tw/images/howto/en/info_pendulum_zone.jpg .
Secondly) pendulum monster is half spell, and half monster, as you can tell by their card colour. If a pendulum monster is placed in either of the pendulum zones (on the left and right) It becomes a "Spell Card" allowing cards such as mystical space typhoon to be used on it. If a pendulum monster is normal summoned, special summoned or pendulum summoned (We will cover pendulum summoning later) It is treated as a monster card.
Thirdly) Pendulum monsters each have their own pendulum scale, this is shown on the mid-left and the mid-right of the card. Here's another 2 pictures for further reference; http://img1.wikia.nocookie.net/__cb20140603103842/yugioh/images/4/48/Pendulum_Scales.png This is what they look like on a card. http://img2.wikia.nocookie.net/__cb20150424104109/yugioh/images/d/db/IgknightCaliber-CORE-JP-C.png . Despite being written in Japanese, This is igknight caliber. As we can clearly see, his Pen. Scale blue is 2< and his Pen. Scale red is >2 also. On other cards, such as http://img1.wikia.nocookie.net/__cb20150424104049/yugioh/images/0/09/IgknightRiot-CORE-JP-C.png Igknight riot here, his pendulum scales are Pen. scale blue 7< and Pen. scale red >7.
Fourthly) This is finally getting to pendulum summoning. Right, so now we have igknight caliber with a pendulum scale of 2< >2 and igknight riot with a pendulum scale of 7< >7. So, you firstly activate igknight caliber in the left zone, and igknight riot in the right zone. So, since this scale is 2< blue as igknight caliber is in the left blue pendulum zone, and >7 red, as riot is in the right red pendulum zone.
Fifthly) This means that you can special summon up to 5 monsters from your hand or extra deck, (We'll cover extra later) but as calibers scale is 2< and riots is >7, this means that the monsters level must be between level 3 and 6. It's the same in the case as D/D/D Hell Armageddon the Cruel End Overlord which has a pendulum scale of 4< >4 and D/D Magical Astronomer Kepler, which has a scale of 10/10. This will allow you to pendulum summon up to 5 monsters from your hand or extra deck between levels 5 and 9.
Sixthly) If solemn warning is used, all pendulum summoned monsters will be destroyed, as usually, when a pendulum monster in either the left and right pendulum zones or those on the field
is destroyed, be it because of Raigeki, or if mystical space typhoon destroys a Pendulum monster in a spell trap zone, they are sent to the extra deck face-up instead of going to the grave. But, in the case of solemn warning being used, they are sent to the grave, not to the extra deck. Oh, and also, If bottomless trap hole is used, all of the pendulum monsters that were pendulum summoned are banished, not just one.
Seventhly) If a pendulum is used as synchro monsters material, it is sent to the extra, if it is used for an Xyz material and detached, it will go to the grave.
Eightly (Extras)) You can activate a left and a right in one turn. In igknights case, you can use their effects to send them to the extra, to get a different one to your hand. You can then place the newly gotten igknight card with 2< in the left zone and an igknight with >7. Use their effects again to get another igknight card to your hand. Activate this new 2< card and a >7 card and you can special summon all of the igknight cards that you have sent to your extra.
Ninthly (Counters)) For countering pendulums, I would highly recommend using Vanity's Emptiness, as it completely rules out pendulum summoning. Marco Cosmos also works very well against pendulums. I would also highly recommend running 3 mystical space typhoons/ Cyclones and/ or Double Cyclones , and also mistake,as it will make igknights highly in-effective. It also works against Qli's to counter scouts effect. Anti spell fragrance is good too, but is slightly situational.
Tenthly (Deck Tips)) If you are considering making an igknight deck, I would highly recommend running 3 mystical space typhoons/ Cyclones and/ or Double Cyclones, as mistake is very dangerous to igknights. Also run 3 calibers and 3 riots. I would not recommend stingers and at most 1 avenger.
Well, that's all for now, hope you understand pendulums now, anything I didn't point out? If so, leave it below. Hope you like this, I put a lot of time into it <3.