OK, it's kind of hard to explain, but easy to do
on the round part, between the gap made by the outer circle, grab the flat part [with the letters] and pull it up towards the rest of the keychain & rotate the outer circlr until it opens..... I type slowly so you probably already have the answer. Hope it helped
Yours looks a bit different than mine, I think it's older but the general idea is the same. That outer circle rotates around until the gap is open.