Internet Cafes
Hotels usually charge way too much for internet use. The plus side is that they should have a reliable connection and often have the English version of Windows.
If you want something cheaper (but a bit dirtier) then try to find an internet café (wǎng ba, 网吧). There are over 100,000 internet cafes in China. You can find them on the side streets in all of the cities. A typical internet café sign contains the characters "网吧" alongside a picture of some videogame character such as those from World of Warcraft.
The government is strict about the operation of Internet Cafes so you may have to show some ID. They may or may not ask foreigners for a "shēnfènzhèng" (ID card, 身份证). Foreign students can show their student card which will be issued by their University. A passport would suffice too.
Hours
Internet cafes are open almost 24/7. However, according to some internet cafe owners, they have to shut down for at least part of the day due to regulations. Some will shut down at night. Some stay open at night and close at about 5 or 6 am when the hardcore gamers go home, and then open up in the afternoon. Some have people pay a night fee and then close the doors and windows at about 12 locking everybody inside until 5 in the morning when they officially open for business again.
Software
The typical computer in an internet cafe has a Chinese version of Windows, Internet Explorer and a bunch of online games.
The Word "Wǎng Ba"
The Chinese pinyin for "internet cafe" is "wǎng ba". The "a" in both syllables is pronounced as it is in the English word "long" and like singing "la la la" in English.
The Chinese characters are "
".

"Wǎng" means net so try to remember that the Chinese character also looks like a net. "Ba" is a phonetic translation of the English word "bar".