You can either install an internal PCI Wireless Network Card which has a small antenna sticking out from it, or buy an external USB Wireless Adapter.
If you decide on an internal wireless card, all you need to check is that the new motherboard has a spare PCI or PCIe slot. Then buy a PCI or PCIe wireless card as appropriate.
If you decide on an external wireless adapter, all you need is a spare USB 2.0 or USB 3.0 slot.
However, wherever possible it's always preferable to use a wired connection to the router if it's close enough to your PC, because it's more reliable, faster, and less hassle than wireless.