There are 2 main forms of connectivity for computers, WiFi or wireless networking as well as ethernet. The obvious difference is that wireless requires no physical connection between machines whereas ethernet, whether Local Area (LAN) or Wide Area (WAN) require connections between machines by cable.
Wireless networking, or 802.11 networking, is becoming more widely used. With WiFi, computers on a network can be 100 feet, or, thanks to advancements made in wireless networking, even farther apart. Wireless works through radio signals and has the obvious benefit of being simpler thanks to the lack of wire connections. There are different standards of 802.11 networking. For example, 802.11b and 802.11g transmit at roughly 2.4ghz while 802.11a transmits at approximately 5ghz, which allows for faster data transfer. In order to access a network or the internet via WiFi, you only need an 802.11 card. You then need to find a hotspot from which to get a data stream connection. These hotspots, however, can be open or secure. Open hotspots alow anyone with a WiFi card to access the network, whereas secure hotspots require the user to have a Wired Equivalent Privacy (WEP) key. Standard encyption types are 64-bit and 128-bit. 64-bit is fairly easy to crack and force unauthorized access to, whereas 128-bit, due to the added security, is standard for a secure hotspot. If you wish to set up your own hotspot, it will require a wireless access point. This is connected to either your ethernet network or cable modem. Most hotspots will cover an area of about 100 feet, but signal boosters are available to widen this distance.
More common, however, is ethernet. Ethernet networks fall into 2 categories, Local Area Networks (LANs) and Wide Area Networks (WANs.) Local Area Networks connect things close together, for example, machines in the same building or on the same floor. Wide Area Networks connects less devices over larger distances, possibly over a dedicated line, for only their data. Fiber optic cables are allowing LANs to connect at distances miles apart and give WANs more reliability. Ethernet is a single network that connects multiple devices, so a new device plugged into the ethernet network would by default have access to the other devices on the networks. The only stipulation is that all devices must be using the same protocol, or standard, so they can share data.