For temporary connections, I solder these:
http://i.ebayimg.com/t/100-pcs-1-x-20-PIN-2-54mm-1-BREAKAWAY-HEADER-PIN-STRIP-FAST-DEL-USA-SELLER-/00/s/MTU5OVgxNjAw/$(KGrHqF,!lEE-j2UWj4YBPt70rZbrw~~60_57.JPG
to either old computer cables or the rainbow colored ribbon cables you can find on ebay and then plug them into corresponding female headers like those found on the arduino. For permanent projects, wires are soldered directly to boards. It also helps to take a few minutes think about the design and where things go before hand.
@ runawaypancake: yeah just like that, you beat me to it