The vast majority of routers are 'wireless'. I'd be very surprised if yours isn't.
Assuming it's wireless, it will be broadcasting its 'SSID'. That stands for it's 'Service Set Identifier' but basically it just means that's what its name is. It's likely to include the name of your internet service provider. (For example, my ISP is a firm called Claranet and my router's SSID is 'claranetsoho').
Ask your partner to use
any device which is capable of using a wifi connection to search for signals at your location. (For example, if I go into the wifi settings on my mobile phone, I can see my router listed there, as well as those of my neighbours. I can also see the strengths of their signals, indicating which are closest to where I am).
If your partner can identify your router that way then it's definitely wireless. The next thing she'll need is its 'security key' (which is just another name for the password needed to connect to its signals). That will most probably be on a label attached to your router and/or in the paperwork which your ISP sent with the router. (If it's not, there a way to find it out via your computer but we'll need the make and model of the router to tell you how to do it).
That's got the router end of things sorted out. Now I'll move onto the laptop:
All modern laptops come with a wifi card built into them. To check whether your partner's laptop has got wifi built into it, ask her to take a look at the icons in the bottom right-hand corner of her screen. (She might need to click on 'Show hidden icons'). If there's a wifi icon there, all she needs to do is to click on it, select the SSID for your router, tick the box marked 'always connect' and then click on 'Connect'. She'll then be asked to enter the security key for your router, which will get her connected.
If your partner's laptop doesn't have a wifi card built into it, then the easiest solution is simply to plug in a USB wifi adapter, such as this one (for just £2.45) from Amazon:
http://tinyurl.com/hfyajtg
Then the laptop will become wireless-enabled and she can connect it to the internet, as above.