I always clean my tired and uncomfortable eyes with the eyes drops with clear role. This way could be effective and useful. If you just clean the eyes with clean water which may contain the invisible bacterium, your eyes may get hurt. You'd better use the eye drops to release your eyes and then use the warm compress to make your eyes feel comfortable.
As the best way to clean your fatigue eyes, there have some suggestions. This symptom of fatigue and dry eyes are usually caused by excessive eyes using. You must be working long time beside to computer or books. You need to relax your eyes every ten minutes for a while. To looking outside for a long distance will help to your vision. The decrease of blink times will cause lack of tear hyposecretion that lead to dry eyes and visual fatigue. When you feel tired, this time you need artificial tears to relief the dry eyes and have a good rest after that. The next time you go to work, please soften your computer screen's light, and lower the intense of contrast, which will ease your eyes. If your work will ask you use computer in a long time, you need to eat some supplement or fruits which full of Vitamin A & B, and carotene. They are the necessary nutrients to protect your eyes in your daily life. Carrot, Chrysanthemum tea, sesame, bean, milk and wheat germ are all the great choice for you to get vitamin which your eyes needs. At the meantime, eyes massage will bring more comfort to your eyes.
Well, it seems that you are got some troubles with the way to get your eyes clean. As far as I know, tap water are not very healthy for your eyes. But I recommend that you just try to get some normal saline. And just try not to rub your eyes, you simply have to drip the saline into your eyes. Also, try to get your eyes fresh by getting your eyes wet with tears, that is also a good way.