When coming out to a family member or close friend, pick a time when you can talk with them privately and undisturbed - a time when you're likely to command their attention. In other words, when they have time to dedicate to you and they aren't preoccupied with other tasks. One time to avoid would be when travelling in a car if you are driving or the person finding out about you is in the driving seat. Whoever is driving should really be focussing his or her attention on the road.
Equally, be sensitive to the timing in terms of the person you're telling. If it's someone close to you, even though you're hoping it won't upset them, you shouldn't tell them just before an important event in their life. For example, as they are about to sit an exam, celebrate a special occasion or when they are dealing with a difficult situation in their own life.
Lastly, make sure the emotional climate is right. Telling your parents just after they've had an argument with you, or with each other, is not a good idea. Avoid times when people have other things upsetting them or preying on their mind, for example if they've just lost their job, or they're about to go into hospital. Equally it doesn't make sense to tell anyone when either you or they are tired.