A router allows a single internet connection to be shared amongst two or more computers.
If you already have a PC connected to the internet then she can use her laptop by simply unplugging the cable from your PC and plugging into her laptop.
She does not NEED a router if you and her are willing to take it in turns to use the internet on the single connection.
If she is staying for a long time, then it probably is worth getting a router.
You ask for recommendation.
Well it depends if you are on an ASDL phone line for broadband, or if you are on Virgin cable. They use different types of routers.
Also, I assume she will be using a wifi connection between her laptop and the router, so you will need to make sure the router is wi fi enabled.
There are a loads of brands that make good cheap routers such as NetGear, LinkSys, d Link and so on.
You can buy a router at PC World or any electronic shop that sells computers and computer parts.
Note that once you get a router it does need setting up, which may seem daunting if you are not very technical.