My step-daughter doesn't have a father on her birth certificate. What can I do to adopt her?

Start by hiring a lawyer experienced in adoption law. It's a complicated process and will take a lot of work. They will know everything that's required based on the laws of your state.

The fact that no father is listed actually makes this harder. The court will require that the father be found and his permission for the adoption obtained. Or, at least, a good faith effort be made to do so. Only after the court is satisfied that the father doesn't object will they approve the adoption. That's why an attorney is absolutely necessary.

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Originally Posted by ScottGem

... Only after the court is satisfied that the father doesn't object will they approve the adoption. ...

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Or, the court could over-rule the father's objection. But yes, OP should get an attorney.