During a recent session, my character was given a Cloak of Protection and a Staff of Fire. Both items require attunement. Is it possible to attune to both items at the same time or do I need to attune to them seperately?
Can you attune simultaneously? No.
Unfortunately, you are limited to just one item per short rest. The basic rules covers this (emphasis mine):
Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties).
You can generally attune up to three in total
The Basic Rules covers this (my emphasis):
An item can be attuned to only one creature at a time, and a creature can be attuned to no more than three magic items at a time. Any attempt to attune to a fourth item fails; the creature must end its attunement to an item first. Additionally, a creature can't attune to more than one copy of an item.
As long as they aren't the same item, a character can attune to up to 3 items. Your character can definitely attune to both the Cloak of Protection and the Staff of Fire (assuming you also meet the requirements for the Staff).