The bible says don't appear unto men to fast, meaning, don't be looking all deep and ceremonious and trying to bring attention to the fact that you are fasting. Go about your regular day, but first anoint yourself and pray and then on the inside meditate and pray while you work or do whatever it is that you have to do.
There's a corporate fast with the church, and then there's a fast where you just do it by yourself. I've done it a few times with friends.
I don't think it's wrong to tell someone, it just depends on your motive in telling it. Are you telling it so they will think you are really deep or spiritual?
I was on a fast not too long ago, and my Pastor's Wife is very insistent about making you get something to eat. So she kept telling me to go get a plate, and I kept saying no. After a while, I just told her I was on a fast. Of course, then she understood.
It's not something that you broadcast, for a lot of reasons, but mainly I think because a primary motive for announcing a personal fast is just a lot of pride, so the old saints used to teach us to keep quiet about it. You don't want to open any doors for the enemy to sabotage your efforts.
Of course, the corporate fast would be different as the whole group would be on it together. I kind of like those because then I can call my friends and we talk about the Word of God and help strengthen each other to go through. The accountability helps you stick to your committment.