>>1202115
Think of Link summoning as a special tribute summon from the Extra Deck.
In order to link summon, you need to use materials (by sending them from the field to the GY) whose link rating is exactly equal to the link rating of the monster you're summoning.
Now, every monster in the game has a link rating of 1. This means that to summon a link-2, you would need to use two monsters, and for a link-3 you would use 3.
However, link monsters also have a value equal to their link rating. Therefore, a link-2 monster could count as 1 or 2 materials, and a link-3 monster counts as either 1 or 3, but never as 2.
So for example, if you want to summon a link-3 monster, you could use a link-2 monster and any other monster. If you want to summon a link-4, you could use a link-3 and any other monster, two link-2 monsters, or 4 monsters in general. If you want to summon a link-5 monster, you can use a link-4 and any other, a link-3 and a link-2, two link-2s and any other monster, but you would not be able to use two link-3s because even though their maximum link rating (6) exceeds the link rating of the monster you're attempting to summon, the sum has to be exactly 5 in this case.
Ah, and every link monster has an amount of link arrows (all pointing in different directons) equal to its maximum link rating. So a link-2 monster has 2 arrows, and a link-3 has 3. These arrows are important because
you can only link summon monsters to empty extra monster zones (the two monster zones between the fields)
or to monster zones a link monster is already pointing to.
If a link monster points to another monster, or if any monster is pointed at by a link monster, it is considered linked. If two link monsters have arrows that point at each other, they are both considered co-linked. These are special statuses that can enable effects and such, like in pic related or like with Knightmares.
And that's the gist of it.