Let´s take an example, if I´m going to a concert or doing something fun, and I want to express how happy and excited I am about this: what would I say in Turkish?

Would I use the present tense or future tense?

I´m not sure what the phrase would be in English even...

"I´m happy" (right now)

"I´m looking forward to it"

"I´m really excited!"

happy = mutlu, I´m happy = mutluyum

excited = heyecanlı, I´m excited = heyecanlıyım

you can say ´çok´ before the word to express a greater degree, like very or really.

I´m looking forward to ... can be expressed several ways

dört gözle bekliyorum (literally - I´m waiting with 4 eyes)

sabırsızlanıyorum (I can´t wait)

iple çekiyorum

Thank you, Henry!