It's like synchro without the need for tuners and you don't need to match levels.
When it comes to link ratings, it means the number of monsters need to link summon a link monster. Example:
Link 1 = 1 monster that fits the summoning criteria.
Link 2 = 2 monster
Link 3 = 3 or more monster or you could use link 2 and 1 non link as materials.
It's actually pretty easy but combo heavy mechanic.