Xbox 360 does it have Wifi? If not, how can you connect to Xbox Live? I have a Wifi Router at home.?

You need to buy the official one. You could just get a 50 foot Ethernet cable for $10 and the connection would be better.

The Xbox 360 has built-in 10/100 base T ethernet. If you cannot use that due to placement, then you can: 1) Buy the $99 Xbox 360 USB WiFi adaptor. or 2) Use internet sharing on your computer.

connect the xbox to the router via an ethernet cable or connect the xbox to a computer with with a wifi adapter, the computer can then share it's internet connection.

Yeah, that adapter is pretty pricey, but if you don't want to run a cable, you'll have to invest in that adapter. Otherwise, you can always get an ethernet cable long enough to run from your 360 to your router. Without either one of these, you won't be able to connect to Live.

you need a wireless router or you can hardwire it or get and original xbox one for 50

Sorry man, you either have to go out and buy one or you have to get a cable which can also be expensive and you have to connect that to your 360

UMM IMPOSSIBLE? UMM UMM YOU TAKE 50FT ETHERNET CABLE BOOM OR TAKE 25FT AND A 10FT BOOM NOT SO IMPOSSIBLE YA U NEED BUY WIRLESS THING UMM BUY USED I DONT HEAR ANY DEFECTS ABOUT THEM SO I WOULDNT TAKE THAT INTO FACT BUYING IT USED UNLESS SOME NUB SLAMED IT ON THE GROUND LOL THEY GO ABOUT 40-50 ON EBAY MABY LIKE 60 USED IN GAME STORES MABY EVEN 40 IN POWNSHOP IF U CAN FIND ONE