Keep dating time and parenting time separate (for non-custodial parents especially). Children need to know that their time is important. Children will often resent the new person if they feel their special time is being intruded on.
Avoid sleep-overs with the new person when the children are present. Viewing you as a sexual being is disturbing for most children. Do not expose your child to this side of your life.
Introduce the new person only when you think the relationship has long-term potential. New relationships might not work out so wait awhile before you introduce the new person to your children. Introducing many people in the children's life creates confusion and insecurity.
Don't have the children refer to the new person as a relative. Telling the child to call the new person Mom; Dad; Uncle, etc., is too confusing particularly if the relationship doesn't work out. Have the children use the first name of the new person.
Go slowly. For instance, introduce the children to a new person first before including them in family activities. A new person who is worth having in your life will understand your need to ease them into your children's lives.