You will be lucky if you are to take care of a below 5-year old. Dealing with brats or those in their peak teenage years could be an extremely testing task.
Nevertheless, there are some basic rules to handle the step child.
Be Motherly/Fatherly, but Friendly
You need to accept that though you may be having parent-like feeling for the child you are not his/her parent. But this is good news. It shows that you have affection for the child which will help you keep patience, much needed in near future.
Your approach should be friendly yet have an air of elderly. This makes the child will feel comfortable with you but at the same time remembers that he/she is talking to an elder person who they should give respect.
Build a Bond with Common Activities
Participate in activities in which the child holds an interest. Volunteer to take them to baseball games or skating classes. Taking responsibility of picking and dropping the child from these activities will give you ample time and opportunity to gel with them.
Children are not expected to behave rationally. They may be holding you responsible for separation of their parents. Even in case of demise of either of their parents, the child may not seem fond of you for the simple reason that, why did their parent re-marry?
Allow them to Analyze and take their Decision themselves
Let them know that you appreciate them taking their own decisions. For example, if the child is having trouble choosing between a baseball summer camp and piano lessons ask him/her to take decision based on what they want to be seen as? Would they like to be a person playing piano or someone playing their best on the field?
Let them take their own decisions.
In terms of facilities, treat your biological and step-child equally. If there is an age-gap between them then you will need to take help of your spouse.