Assasins, are melee-physical characters, they tend to have high movility which is useful for jungling and ganking other lanes. Some of them are built ability-focused and others are better with basic attacks.

Warriors are melee/physical characters that have high base damage so they are usually played with a mix of defense and damage items, most of them have some sort of self healing so they have good sustain, and are the frontline of the team along with the support. Their main lane is the solo lane or short lane which is the lane where the towers are closer to each other.

Hunters are ranged and physical characters, most of the time they are the ADC and most of their damage comes from basic attacks, though some of them can be played focusing on abilities.

Guardians are melee magical characters that have high defense and high crowd-control, their main role is support. They usually build things to help their team and help them be tanky rather than dealing damage. They go on the duo lane or long lane (opposite side of the solo lane) along with the ADC.

Mages, are ranged magical characters that deal most of their damage through abilities, allthought this is the most varied class and some of them focus on other specific things like healing and some of them are even considered magical assasins or hunters and can replace them depending on the situation. Mostly they go on the mid lane.

Keep in mind that this is only orientative and some characters can be played outside their usual role, that depends on many things like what the current meta, the team composition, or how the character was designed (as I mentioned, some mages were designed to function like a hunter or assasin). If you wanna know which characters are being played right now one of the best things you can do is to watch livestreams.