Searching: try 58.com, Beike Zhaofang, Ziroom, or an agency. Foreigners usually rent apartments or gated-community flats. When viewing, check: how far to the metro? Is there a supermarket downstairs? How are utilities billed?
Signing: read the rent, deposit (usually one month deposit plus three months rent), lease term and repair responsibilities carefully. A bilingual contract is best, or have a Chinese-speaking friend review it. Your passport is your ID.
Within 24 hours of moving in, complete accommodation registration at the local police station (a legal requirement — very important). When you move out, get your deposit back and settle utilities first.