Most group health insurance plans have scheduled open enrollment periods when changes can be made to your policy. Additionally, there are certain life events which allow you to make immediate changes to the policy. If you've got an individual plan instead of group coverage, the rules are different, but there are other considerations to be made. In the case of a new marriage, you should request the changes as soon as possible, though, because you only have a limited amount of time to make them.
Marriage, birth and adoption are both 'triggering" life events that allow you to make immediate changes to your health plan. You policy will provide you with a full list of triggering events, or contact your insurance company if you have a question. For your new marriage, contact your Human Resources department or the insurance carrier and inform them of the change in your marital status. The representative will provide you with the forms necessary and any additional information you need to add you wife.
Typically, you have 30 days to file for changes based on triggering events. During the period, you can request changes such as adding or removing family members, otherwise you will have to wait on the next open enrollment period. Check your policy for when the next open enrollment period is for your insurance plan.
If you have an individual health insurance plan, you can request changes whenever you want to make them. Individual plans are different from group plans, though, and your bride and step children may be required to take medical exams before they can be added to the plan. Additionally, anyone has a preexisting condition such as asthma may be denied coverage because individual insurance plans tend to have much stricter guidelines for who qualifies for coverage.