To say that something just happened use venir de before the infinitive form of the verb.
Nous venons de manger.
We just ate.
Elle vient de se réveiller.
She just woke up.
Ils viennent de faire un gâteau.
They just made a cake.
In English we might say I am waiting for Marie, but in French you can just say J’attends Marie.
J’attends Marie.
I am waiting for Marie.
Nous attendons notre collègue.
We’re waiting for our colleague.
Vous attendez le bus ?
Are you waiting for the bus?
In English we can say I gave the letter to Noemie or I gave Noemie the letter, but in French, you always have to say I gave the letter to Noemie.
This is the case even for verbs we don’t use to with in English, like répondre or demander.
Nous donnons une lettre à Émilie.
We’re giving Emily a letter.
Il demande une information au vendeur.
He asks the sales associate for some information.
Elle répond au téléphone.
She answers the phone.
Il écrit une lettre à ses parents.
He’s writing an e‑mail to his parents.