There are several solutions for your problem, and they have huge price range and complexity differences. I'll cover the conceptual basics here and the issues you may come across. I am assuming that your question was literal; you are attempting to that a mic signal from a singer and send it back to her with some effects on her voice without recording her voice whatsoever. If you ARE recording the voice with the same computer, this changes the procedure.
So the easiest way to do this with a PC is to use the following chain:
Mic -> Preamp -> A/D Convertor -> Standalone Reverb Application -> D/A Convertor -> out
For this solution, you would need a audio interface to handle the A/D D/A task, and they often also have a preamp built in. There are many out there, ranging from $50.00 to $3500.00, so I would say that a specific model recommendation would require more detail from you.
As far as software goes, standalone reverbs are relatively rare, since most people use reverb software as a plug in. The best freestanding 'verbs use convolution engines. In my cursory search for this answer, I couldn't find a non-plugin app, but I know that they are out there.
The second, slightly more complex but much more available solution:
Mic -> Preamp -> A/D convertor -> plug in shell -> reverb plug in -> D/A convertor -> out
Since most reverb software is designed to work within a host DAW program, you need a platform upon which you would host the reverb. On PC, I would recommend using VST Host. The world is then your oyster in terms of software choices. There are phenomenal reverbs from Native Instruments, Waves, UA, and many others. Here's a nice guide: Ultimate Guide to Reverb.
There are also a plethora of free plug in offerings. Here is a slightly outdated list: 15 totally Free Reverb plugins
There are also a few platforms that are full blown recording apps in their own right that just happen to have facilities to use their effects live. Logic on OSX and Reason/Record are two that come to mind, but there are many, many others.
The biggest problem you are gong to face is latency, which, depending on how you are monitoring the audio going back to the singer, can render this entire exercise unusable (this is not hyperbole). You can reduce latency in many ways, and a combination of methods is usually best:
- Use the fastest computer you can get your hands on lots of RAM.
- Reduce the i/o buffer size in the audio interface's control panel.
- Streamline your computer in terms of extraneous extensions, dlls.
- Augment your processig power by using an interface with a built in DSP chip or a box dedicated to processing the plug in.
- This goes beyond the scope of your question, but you could also just get a hardware reverb.
OK so for YOUR application, it's unclear what you need. You last sentence doesn't really specify whether this is for a live performance context, recording to another platform while providing effects from the PC in question, or recording onto the same pc that is providing an effected feed for the singer. If you clarify it, I can make more concrete suggestions.