First of all, welcome to Yu-Gi-Oh! If you’re not new to the game, then welcome back. The field has gone through a few changes in the past couple of years, with the introduction of Pendulum Zones in 2014, and now the entire field has changed with the introduction of Link Monsters!
The new field has done quite a lot for the way the game is played. Let’s start with what has remained the same. You still have five monster card zones, (now called “Normal Monster Zones”) and your deck, extra deck, graveyard, banished, and field spell zones are all in the same place with the same mechanics. However; while you still have five spell and trap card zones, two of them now double as "Pendulum Scale Zones". These are the zones to the far left and far right of your spell and trap zones. This means that if you have two pendulum monsters on your scales, you now only have space for three spell or trap cards. Aside from this change, the field also has two new zones known as “Extra Monster Zones.” While there are two, one is for you, and one is for your opponent. This zone is where you will summon monsters from your extra deck. This means, that unless you use "Link Monsters", you can only use one monster from your extra deck at any given time.
Now if you already know what a "Link Monster" is, how it works, and all the mechanics involved with it, you can skip this section; however if you don’t, I encourage you to read this. A "Link Monster" is a new type of monster with a blue card background, no level, no defense ("Link Monsters" cannot ever be in Defense Position, no matter the circumstances), and arrows around the card pointing in various directions. On the bottom right of the card, there is a “Link Number.” This is the required amount of monsters to summon this card from your extra deck. Summoning a "Link Monster" is a matter of simple math. When using "Regular Monsters" with levels (Any monster other than a "Link Monster") You simply need to add up the number of monsters you’re tributing in order to match the "Link Number" on the "Link Monster." If you use a "Link Monster" to perform the summon that monster's "Link Number" is used instead. So for example, if you want to summon the Link-3 "Decode Talker", you can use one "Main Deck Monster" and one Link-2 Monster to summon it. 1+2=3. When summoned to the field, the "Link Monster" opens up the monster card zones where the arrows point, so that you can now special summon to these zones from your extra deck. So if you summon "Decode Talker" to your "Extra Monster Zone", the far right and third from the right “Normal Monster Zones” are now also “Extra Monster Zones.” So, you can then summon a Synchro, Fusion, XYZ, Link, or Pendulum Monster from your extra deck to those “linked” locations.