What's the difference between "o yüzden", "bu yüzden" and "yani", and when should I use them?
I see these words all the time and for me, it seems they are used in the very same situations, but I guess that there are some differences.

Question

Answer

O yuzden = bu yuzden = this is why, because of that

Yani = in other words

Answer

Sabah uyanamadım, bu yüzden geç kaldım.
Sabah uyanamadım, o yüzden geç kaldım.

I couldn't wake up in the morning, that is why I am late.
I couldn't wake up in the morning, therefore I am late.

Answer

yani
in other words, I mean, in better words, so

Answer

.
yüz
1face
2aspect, reason, fact

o yüzden
for that reason; that's why

bu yüzden
for this reason; that's why

Answer

"o yüzden" means "because of that"
"Bu yüzden" means "because of this"
"Yani" mostly means like "I mean" 
But make sure that the usage of "yani" is really wide. You can use when you wanna say "so", "how", "of course" and more