Formal:
* Я знаю (Ya znayu) - This is the most common and general way to say "I know".
* Мне известно (Mne izvestno) - This means "It is known to me" and is a more formal way to say "I know".
Informal:
* Я в курсе (Ya vkurse) - This means "I'm in the loop" and is a more informal way to say "I know".
* Я понял(а) (Ya ponyal(a)) - This means "I understood" and is often used to acknowledge that you understand something.
* Я догадываюсь (Ya dogadivayus) - This means "I guess" or "I have a hunch" and implies that you are not completely sure but have a good idea.
Other variations:
* Я осведомлен(а) (Ya osvedomlen(a)) - This means "I am informed" and is a more formal way to say "I know".
* Я в теме (Ya v teme) - This means "I'm in the know" and is a very informal way to say "I know".
The best way to choose the right phrase is to consider the context and your relationship with the person you are speaking to.