How to convert negative NMEA latitude and longitude values ('S' and 'W')?

Have a look at this tutorial. It may be able to help you out. Also, depending on how you are getting the data, you may have built in ways to convert it. For instance, if you're reading the NMEA stream via something like a Trimble SDK, they usually have converters in there.

I also remember that if you're using a .NET program, there were numerous converters out there as open source. For my application build in .NET, I ended up just writing my own algorithm to convert NMEA streams to decimal degrees.

This post outlines some programming parts to it. If you're not looking to use a programmatic method to convert it, there are converters online such as this one from the US FTC.