If you are close enough with the child, you might be able to talk to them about it. Asking the right questions can help you learn more about what is happening to them. Here are some ways to go about it.
The environment
The best way to talk to the child is to bring them to a non-threatening environment where they are most comfortable in. Pick a time of day where they have the right amount of emotional energy to communicate with you. Avoid talking to them if the suspected abuser is infant of you and the child or in hearing distance.
Starting the Talk
Be aware of the tone of voice you have with them. Starting in a serious tone might intimidate the child into not wanting to answer honestly. Minors can ready body language and tone more than people expect, so making sure you have no judgment or blame for the child will help them feel comfortable. Talk directly; make sure to use vocabulary that they are familiar with and stay vague in the beginning of the talk by asking basic questions like "are they touching you?" Sometimes the child doesn't understand that the abuser touching them is a bad thing, some may even think it feels good and is a game. So if you ask questions that immediately put the abuser in a bad light, the child might be confused.
Let the child communicate back; let them answer the questions and gradually ask for detail. Along with answering, you should also let them ask questions or give responses that seem irrelevant to you, sometimes those responses can be explained and be related to the issue. Making sure to be patient through out the conversation can help the child gradually give more information.
Reassure them by letting them know they are not in trouble is an important part of talking to them. If they were threatened by the abuser they may be horrified to get in trouble, telling them that everything is okay can let them not feel shame.
If they admit to being sexually abused, do not react strongly or display any sort of anger. Once the truth is out your behavior will play a big role in the healing process for them. Saying phrases like "I believe you," "it's not your fault," or even "I am proud of you telling me, you did a good job," can indicate to the child that they are being supported.
Reporting
If you and the child are in a place where you both have strong communication with each other, letting them know that you have to report to the authorities can prepare them for what is possibly to come, especially if it is a family member who is the abuser. If it is hard to find the words to tell them, you can say. . .
"I am glad you told me your secret, but I am going to have to tell some other people so we can help you and protect other children as well."