I haven't seen networking for dummies but I would think it would be helpful. I have a D-Link DI-524 wireless router. But, I don't want to get into recommendations because this is the only wireless router I've owned, so I don't have experience with other models for comparison. However, I will say I've had no problems with this router; I bought it about 5 months ago, as I recall.
Like many other routers, my D-Link DI-524 has ports on back for up to 4 computers via cable. This is in addition to the wireless part of it. So, yes, your grandma's computer could be connected to it via CAT5 cable. If her computer does not have an onboard LAN/ethernet connector, you can get ethernet car to install in a PCI slot. They are not very expensive.
What type of Internet service do you have? DSL, cable, dialup?
When you connect a router to your modem, you may need to change your modem's configuration to work with a router. At least, this is what I had to do with my DSL modem. Fortunately, I was able to get telephone support from my ISP on setting this up, at no additional charge. I believe some ISP's are fussy about this. You might call them and ask them whether settings in the modem would need to be changed if you add a router. See how they respond.
