I'm new to coding so this may be a stupid question but I have three different style sheets for my website. Each one shows the presentation perfectly for it's intended browser. I'd like to know if it's possible to do a browser detection and upload the appropriate style sheet for the compatible browser. If not, how do you guys do it? Where do you put the alternate pages?

Yes, it's possible.
Most of us would not do 'alternate' pages I think, especially if the layout is the same but the stylesheet is the only thing that's changing. There are scripts out there for stylesheet 'switching'.