If you have a wireless router in your house already, then it's an easy business. You'll have to go to the internet connection menu on your 3DS, search for the same access point as your router (A.K.A, your router's name) and then input the password that you have for your connection.
The 3DS is much easier to connect via vireless because it not only accepts WEP passwords, but also WPA, WPA2, WPA-Enterprise and WPA2-Enterprise passwords, and it has a 801.11 b/g/n capacity.
If you don't have a wireless router, you'll need to get your hands on a wireless USB connector (the Nintendo Wi-Fi USB connector is good, but I don't think those are sold anymore), which in this case, any Wi-Fi USB connector works, you just need an USB Female A type to USB Mini B 5 Pin type adapter (these are very cheap).
To work with that system, you'll need to have an external wireless USB adapter coming out of your internet cable-connected PC and have the USB connector in your 3DS configured to your internet specifications the same way as if you were using a wireless router.
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
