In many jurisdictions it can take hours before a person who has been arrested is allowed to make a phone call to let someone know of his predicament. So it useful to know how you can find out if she was arrested and prepare to make arrangements for bail or an attorney if necessary.
Where to start
Find the phone number for the local police district in your phone book or call Information. Ask for the non-emergency number. If you live in a town with only one police district or you know the person never strays outside of that district, this would be the first place to start.
Explain the reason for your call when the police answer the phone, and respectfully ask if the person you are looking for is in custody. If they have him, they should tell you. If they don't have him, they will ask when he was arrested and may ask why you think he was arrested. If it was very recent, he may not be back in the police station yet, so you may be asked to call back.
Look up the number for central booking--do this if the police say they don't have her, or if you think they do but aren't telling you, or you live in a large city with many police districts, which makes it impractical to call them all. Typically the police have a central point that all districts have to report arrests to. This is particularly true in large cities. Central booking almost always gets notified of arrests fairly quickly.
Tell the person in central booking who answers the phone that you want to know if someone has been arrested. They will ask you the person's name and possibly date of birth, to be sure they have the right person. If he is in the system, central booking can tell you at what district he is being held. They may or may not tell you what he was arrested for.