Wireless Access Point
Technology
The technology behind Wi-Fi isn't very exciting. The devices just uses a unregistered band of radio waves to transmit data just like any other wireless device, such as radios and walkie-talkies.
Wi-Fi has several different standards of varrying speeds. IEEE 802.11 b and g both operate at the 2.4 Ghz band, while a operates in the 5 Ghz. IEEE 802.11 a and g both have a max data transfer rate of 54 Mbit/s, while b has a max rate of 11 Mbit/s. IEEE 802.11b was the first popular frequency, but g is gaining in popularity due to the fact that it's in the same band allowing it to have easy legacy support.
802.11n offers much greater speeds, but isn't in its final form yet, so it's too early to start supporting it.
What's Needed
The first thing to do when you want a wireless network is to make sure that all computers that will be connecting to network have wireless network cards installed, and they all support the same wireless standard. The next thing you need to is to create (Ad Hoc), find (some cafe), or buy a wireless access point(wireless router).
Wireless Router
Using a wireless router to create a wireless network is the easiest way to create a wireless network. They generally come with enough setting pre-configured for you to connect to it right out of the box, and configuring them to connect to the internet and giving them adequate security settings is very quick and easy.
Ad Hoc
Ad Hoc networks, or wireless networks without routers are also an option. You can have one computer connected to a modem through a Ethernet port and have that computer share that connection through its wireless card. The advantage of this type of network is not having to buy any equipment (unless you don't have a wireless NIC installed on all your computers.) The disadvantages are that one computer has to always be on, it's a little less reliable, signal strength is generally weaker than what you would get with a router, and security settings (such as enabling WEP) can be tricky. It sounds like this has a lot going against it, but with wireless routers costing 30+ dollars it's worth considering.
An extension of this type of network is a Wireless Mesh, where all computers share their connection enabling one access point be extended over considerable distances. This is how the 100$ laptop will try to spread the internet throughout unconnected parts of the world.
Security
Security for Wi-Fi networks is much more of an issue than it is for wired networks. With Wireless networks anybody within range of your access point can detect it, and if it's unsecure than they could see (sniff) the packets that are going between your computers and routers. This could easily lead to someone gaining some of your personal information.
There are three main encryption methods used in wireless networks. WEP is the most common and simple method of protection. It has some weaknesses, but it's probably good enough to stop someone from spying on you or gaining access to your network. WPA and WEP2 both offer increased security, many old systems don't support either, and Windows XP needs an update for WEP2.
If you have a wireless router, the first thing you sholud do is change the User name and Password needed to configure the router. You can assume anybody who would be trying to connect to your network knows the default usernames and passwords used on routers.
If you feel the need for extra security you can always make your router filter who can use the network by IP or maybe even MAC address.