Connecting 2 Buildings

Regular wifi or ethernet won't work at that distance. There are basically two realistic options - optical fibre or point-to-point wireless. Point-to-point wireless uses similar tech to normal wifi but optimised for a a single long-distance connection as opposed to covering an entire albeit smaller area - you'll have an access point and high gain antenna, usually externally mounted, at both ends of the link, and you'd generally need line of sight between the two buildings. Optical fibre would need a pair of fibres laying however is appropriate in the particular situation - underground, along a fence etc. Twisted pair→fibre converters do exist but most people would simply specify a switch with a suitable fibre interface at end end.
Copper Ethernet is limited to 328 feet (100 meters) so it's off the list. 

Fiber optic can easily handle 600 feet, but it is relatively expensive (compared to other possible options) and is somewhat fragile. Ideally the run should be buried in a properly installed conduit. If bandwidth is important, this is your best option. 

There are a number of wireless solutions that will be less expensive to install than fiber, though not cheap by any means. Cisco makes several wireless bridges that support 802.11b/g/n speeds. A simple, inexpensive yagi antenna at each end will easily span 600 feet at full speed. An unobstructed line-of-sight is essential for wireless, however. With the right antennae and wave guides (a specialized by of cabling that has lower loss than coax) distances of over 20 miles are possible using the unlicensed spectrum. 

I would strongly recommend that you bring in a skilled consultant if you are not familiar with network design criteria. They do cost money, but a good consultant will save you money by getting your network up and running in minimum speed and without wasting money on trial and error solutions.
There really shouldn't be a need to physically connect them. Connect both buildings to the internet, and...