Bináris,
to claim or assign a task, you have to go to a particular task, then at the end click on the "Add action..." list, then "Assign / Claim" and write your account name or someone else's (it will autocomplete).
Oh, that's pretty hidden in hell! As far as I remember, last time I was looking for it, it was on the right sidebar. At least claiming.
Please note that assigning a task to someone without any previous interaction or context is generally considered "bad etiquette" by most people or teams, unless so documented.
Of course.
Thank you!