Very few computers come with printed literature now, other than a "quick setup guide" so that you can know how to turn the thing on and start using it. Other documentation is either included on a CD or is in a folder on the computer's hard drive. That quick guide should tell you how to find a more detailed manual.
Laptop computers aren't different from desktops, except that everything is in one package. You still turn on the power, wait for Windows to start up, and click on things just like you're used to. Sometimes it takes a little time to adjust to the touchpad on a laptop when you're used to a mouse,. The same may be true for the keyboard since the keys don't have the same travel as a desktop's. But you can plug in a regular mouse or keyboard (or both) using USB ports if you want. Some people do that if they're using the laptop at home on a desk. Otherwise Windows is still the same old Windows.
Just like with a desktop, a laptop needs some kind of connection to the Internet for Web access. Most people now have high-speed "broadband" Internet service through the cable or phone company. A device called a modem makes the connection between your computer and your service provider. The link from the modem to your computer, the local network, is called an "Ethernet" connection. This connection can be done with a cable that plugs into jacks on the modem and computer. An Ethernet plug looks like a regular phone plug, but bigger. In the picture below, the Ethernet plug is on the left with a regular phone plug for comparison.
Because a laptop is meant to be portable, they all have wireless Ethernet capability ("wi-fi") built in. The wi-fi circuitry in the laptop scans for wireless networks and gives you a list of those it finds. You pick the one you want to use, the connection is made, and you can surf the Web without wires. Most Internet service providers supply a modem with the wireless capability included so you can have your own wireless network at home. Your service provider should help you set up the network when they install service, and many sites offer detailed "how-to" information.
Most laptops still come with a dial-up modem as well, so if that's how you've been making your Internet connection you still can go that way. (Don't laugh! Some people still use dial-up service because it's good enough for them. Also in some remote areas it may be all that's available.) In addition to the Ethernet jack, the laptop will have a regular phone jack for that connection.
As for battery use, the time it takes to charge the battery depends on the battery and the laptop. Laptops typically show an icon near the clock at the bottom of the desktop, showing you the state of the battery's charge. It may take anywhere from one to several hours to fully charge. The time you can run the laptop on battery power also varies depending on the battery and computer. The manual (which should be on the computer or a CD, remember) should give you a general ideal of the times for your computer.
I hope this helps clear things up for you. If you have more questions, just post a comment and I'll try to to help further. Thanks for using Fixya!