If an older (i.e. ages 6-12) child refuses to go to time out or leaves time out early, withhold a preferred activity or other reinforcer until the child completes the time out. For example, "You have no TV until you do your time out." If they continue to refuse, withdraw another preferred activity. Do not withdraw more than two activities. These activities must be withheld until the child does timeout or until the next day. Do not carry the consequence into the next day, as this is too far delayed to be effective.
When time out is over, you may say, "Time out is over." Do not counsel or discuss the behavior that results in time out. There is no evidence that discussing the infraction adds any positive effect to time out, and it may even reduce the effectiveness by providing attention at the end of the process.
If the child is still crying or shouting at the end of the time out period, set the timer for one more minute (or two additional minutes for a child over 6). Repeat this procedure, as needed, up to three times. Say only, "That's X more minutes for you to quiet down." and do not make eye contact. If the crying or shouting persists beyond this point, just ignore. (In no case should the child be allowed to leave time out without loss of a preferred activity unless they have been quiet for a minimum of 30 seconds.
Start by using time out for only one behavior and plan to use it consistently for at least four weeks. For children 4-12, describe the time out procedure with them before you try to implement it. Expect objections. Ignore them and do not negotiate. If you must speak say only. "We're going to do this." If objection persist, walk away. Do not engage in a debate.