I have tinnitus in both ears thanks to my MS. It is unbelievably annoying in the beginning, but believe it or not, you actually get used to it after a while.
The worst thing to do is to try and drown it out. The best thing to do is to accept it - there is no treatment and it ain't going anywhere, so better to get used to the new sound of silence! However, if you are struggling to sleep because of it, you can buy things like long playing white noise, rain, wind, etc, noises which, when played quietly, help to mask the tinnitus.
The reason it's a bad idea to try and drown it out is because of the way the brain works. Basically, the brain ignores stimuli that are constant - it is much more interested in change. (That's why you don't feel your clothes or your watch or jewellery on your skin all day; only when your attention is drawn to them.) So, crazy as it might seem, it is best to try and always be able to hear the tinnitus noise. Playing something that is always subtly changing keeps the brain focused on it instead of the tinnitus and so the tinnitus isn't processed so strongly and stops bugging you! If you change your concentration to focus on the tinnitus, it will suddenly seem much louder - this is because the brain is now focused on that noise, processing it as if it is important to you.
Of course, there are physical causes of tinnitus which can be fixed, so if you haven't seen ENT, you should - it might be fixable!