These two words usually indicate direction in relation to the speaker or the listener.
Take implies moving something from where the speaker or listener is.
Bring implies moving something to where the speaker or listener is.
Can you take my dress to the dry cleaner’s?
You can bring it back when you come next week.
Should I take some flowers to Mary’s party?
Don’t take your car to work today. There’s an awful traffic jam in the centre.
Bring the salt, please!
Wait a second! I’ll bring you your towel.
In the last sentence we look at the situation from the listener’s point of view. In other words, we have changed the perspective as in the following examples:
I took your briefcase home with me by mistake.
Thanks for your kind invitation. I’ll be happy to come. Shall I bring some wine?
To sum up, think of movement to or from a position. You can compare with come and go. You come here and you go there. Bring it here and take it there.
That said, you may find that either take or bring is used when the direction is unclear or unimportant. It can also depend on whether you put the emphasis on here or there, if you think about where you are now or already imagine yourself at another location.
When you say ”Should I take some flowers to Mary’s party?”, you are still at home. When you say, ”Shall I bring some wine?”, you are already imagining yourself at the party.