You can get extensions for US$10 at the Jefatura Provincial de Migracion in provincial capitals - it's often at the same address as the police headquarters - and in Quito at Isla Seymour 1152 and Rio Coca (Mon-Fri 8am-noon & 3-5pm). You can't be granted an extension until the day on which your tourist card runs out; there's a small fine if you renew it after it's expired. Extensions are given at the discretion of the relevant official in batches of thirty days, up to a maximum of 180 days per twelve months. It's unusual that you'll be refused an extension, but politeness and smart dress certainly won't harm your cause. In some cases you'll be asked to prove you have enough money to stay in the country for the length of your extension.

You should carry your passport , or at least copies of the important pages, with you at all times - if you can't produce adequate identification on demand you may be fined or even be detained. In some sensitive areas, particularly the Oriente, only the original document will suffice.