You have three options. You can either use WiFi, ethernet cable (which you've said you don't want) or Powerline adapters. The latter uses your normal electrical outlet to transmit the signal and is generally more stable than wireless and shouldn't reduce your connection speed at all because it's wired.
For wireless, you can either get an internal wireless card or a USB dongle. I believe (I may be wrong) that network cards have the potential to be quicker than a USB dongle. However, it would necessitate removing the cover of the PC to install it, which some people don't like to do. Once it's in, though, it stays there and you need never worry about it again
. A USB dongle has the advantage of being plug and play and you can remove it (should you wish) and connect it to another device at any time. They can also be very small, too, and not all are that noticeable when they are in place.
A lot depends on where your PC and router are placed and how far away from each other they are. Other things also come into play like how many walls are between the PC and the router and, if you choose to go the wireless route, how new your router is and what standards it supports (e.g. 802.11n, ac etc, as well as whether it's dual band or not). Finally, your usage requirements are also important (e.g. will you be doing a lot of gaming, streaming, transferring files over your network etc etc).
Can you provide more info?