How should I go about making 80's style graphics?
There are a few things you can do to get this look, first, use an artificially low resolution.  A lot of early graphics generators were done on things like the Amiga Video Toaster at 320 by 240 resolution.

Additionally, you can get the background look by making a normal gradient in Photoshop and then reducing the color depth substantially.  You can either reduce to 8 bit color or simply use a GIF with dithering turned on and lower the number of colors until you get the desired result.

Use classic pixel fonts for the lettering.  There are literally hundreds of possibilities out there to choose from, so you best bet is to look through something like Google fonts until you see something you like.

Finally, use interlaced video and run a couple interlaced to non-interlaced and back conversions to add the scan line related issues typical of old footage.  If you have an old VCR, try recording the video through a couple generations of VCR recording too and it will give it some nice analog degradation to really maximize the feel.