First and foremost, you need to reach level 60 on a character to unlock the Paragon system. In Diablo Immortal, the Paragon levels acquired are not shared between characters, a big change from Diablo III.
Once you hit level 60, you will acquire one Paragon point every time you level up further, with escalating XP requirements the further you go.
There are two types of "nodes" you can spend Paragon points in on each tree, namely Persistent Attributes which are always active on your character, providing stat bonuses and more.

Then, there are Paragon skills, and they are only active as long as a certain Paragon tree in Diablo Immortal is selected.

Not every Diablo Immortal Paragon tree is available once you reach the max level and then level up one more time. Instead, some Paragon trees only open up once you reach a certain Paragon level.

Below, check out the Diablo Immortal Paragon trees, and short descriptions of the attributes and skills you can expect to find in each one.

Survivor tree: Unlocks at Paragon Level 1 - This tree focuses mostly on defensive attributes and skills.
Vanquisher tree: Unlocks at Paragon Level 1 - Focuses on offensive attribute bonuses and skills.
Treasure Hunter tree: Unlocks at Paragon Level 50 - Perfect tree for those who focus on farming, focusing on attributes and skills for Gold and Magic Find, as well as Experience bonuses.
Gladiator tree: Unlocks at Paragon Level 100. This is the PvP-focused tree with skills and attributes that you shouldn't really desire for most PvE encounters.
Soldier tree: Unlocks at Paragon Level 150 - A jack of all trades tree, focusing on both PvE and PvP bonuses and attributes for both Solo play and group play.
Mastermind tree: Unlocks at Paragon Level 150 - Skills focusing on group buffs and diverse permanent attributes. The only Paragon tree to be added since the Diablo Immortal Closed Beta.