Minecraft wiki entry for Setting_up_a_server, associated text: Setting up a server takes some time, and some technical knowledge. Don't try to set up a server unless you have some basic computer and networking abilities. Probably, your best bet can be to look on the Internet for a guide on how to set up a server.
A Minecraft server does not need to be a high-end machine, but netbooks and notebooks don't usually make for good server machines. They typically have lower-end hardware and bad I/O performance in comparison to desktop computers.
Hosting and playing on the same machine is also possible, if your computer is powerful enough.
Having many players in a wireless network (WLAN and especially WWAN) is not recommended. Use a wired network instead, such as Ethernet.
If you decide you don't want to host, but still want to play online, check out the public server options on a Minecraft server listing website.
If you still want to manage a server, but not from home, check out the Minecraft server hosting area of the Minecraft Forum or other websites. Expect to pay monthly for this type of server since finding free hosting is a rarity, but you save the hassle of constantly maintaining a server and ensure it is always online for your players.