Your question did not make clear whether you were wanting to add a dependent to a group or an individual health insurance plan. However, if it is not the open enrollment period for your employer's group plan or you missed the recent individual plan open enrollment period, then you and/or your dependent will have to have experienced a "change of life status event" to qualify for being added to your coverage. While there are more, the most common examples are marriage, divorce, child birth and loss of coverage under another group or individual health insurance plan. Also, as a general rule, you have a 60-day window after the qualifying event to enroll an eligible dependent onto your coverage.
If you are wanting to add a dependent to your employment based coverage your HR person, office manager or the company's insurance broker should be able to assist you with the addition of your dependent to your coverage. If you are seeking to add a new dependent to an individual health insurance policy that you have then you should contact your insurance agent or the insurance company's member services to unit (there should be a toll free telephone number on the back of you ID card) to get assistance in adding your new dependent. If you purchased coverage directly through HealthCare.gov, well, good luck, you are kind of on your own with a government bureaucracy to deal with on top of the insurance carrier bureaucracy.
If you are wanting to add a dependent to your employment based coverage your HR person, office manager or the company's insurance broker should be able to assist you with the addition of your dependent to your coverage. If you are seeking to add a new dependent to an individual health insurance policy that you have then you should contact your insurance agent or the insurance company's member services to unit (there should be a toll free telephone number on the back of you ID card) to get assistance in adding your new dependent. If you purchased coverage directly through HealthCare.gov, well, good luck, you are kind of on your own with a government bureaucracy to deal with on top of the insurance carrier bureaucracy.