Hey guys,  first day on roku and I'm not sure how to connect my PC for streaming. I've checked my network settings. Made sure both connections are on Wifi. I'm not sure how to get my windows 10 to discover roku premium + for streaming.

You connect your Roku to your network not to your computer to get stuff to stream and you connect to a TV or other display device via HDMI for display.
 
You should have received a "quick start guide" with your Roku. Follow that as close as possible.

It is connected to my TV and connected to my wireless network. I can not discover it from my PC even though we are on the same network.

It doesn't work that way.

https://www.youtube.com/watch?v=61eD6FiDPDU
https://www.youtube.com/watch?v=hKhyUX2WNGI
https://www.youtube.com/watch?v=nXMy_PJLeZE

What do you mean?  I just don't know how to make roku discoverable

You are mixing terms.  The ROKU is not a discoverable device on your network.  It does not work that way.  An APP that is a remote?  

If you are talking about Screen Mirroring that's not being discovered on your network.

Screen mirroring through PC only works on specific graphics cards that have wireless projection drivers. If you have enabled screen mirroring on roku and on your PC you go to project to wireless screen it should show up as a device. If not make sure you are on the same network and if that doesn't work it means your graphics card doesn't support wireless projection.

I just got my 75C803 set up.  I previously had a Sony TV connected to my HP computer for 8 years.  I have movies on my HP and I would watch them on my Sony.  Now the HDMI I plugged my VGA display adapter Cable into does not recognize the TV.  So it is not made that way?  Thank you for your help.

Windows computers only support Miracast, which has only so-so support by Roku. Also, there is specific PC hardware requirements for Miracast to work. As I recall, it requires specific support in the wireless card, and also the video card. Most people find their computers are lacking one or both.
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I've connected computers to TVs often with HDMI, and never had an issue. However, I've never used an HDMI to VGA adapter, so your new set might not like it.