Today the national elections council (Consejo Nacional Electoral or CNE) published the official rules for foreigners living in Ecuador who want to vote in the next elections. 

Any foreigner older than 16 who has lived in Ecuador for more than five years and has registered as a voter is eligible to participate in the February 2014 sectional elections.

In order to register to vote, foreigners need to provide the following:

An original and a photocopy of ones passport and "cédula" ID card.
An Immigrant Visa that confirms legal residence in the country

The "five years" mentioned in Article 1 will be counted from the date of issue of the persons immigrant visa, in any of its categories. Ecuador grant non-immigrant visas, but only people with immigrant visas can participate in the elections. (According to this article, those visas are: 9- I Retired persons, 9-II Real estate and securities investors, 9-III Investors in industry, 9-IV Technicians under contract, religious workers, or foreign journalists, 9-V Professionals with university degrees and 9-VI for economic dependants of other 9-series visas.) 

To register to vote, foreigners must go in person to the provintial delegation of the Consejo Nacional Electoral, or show up at the mobile change-of-address stations with the original and photocopies of the relevant documents.

The following details will be included in your voter registration card:
Full name
Nationality/country of origin
Place of residence (province, cantón, parrish)
Type of visa
Date of birth
Date of issue and expiry of the visa
Cédula number
Passport number

The system will generate a print-out, which the applicant and the CNE employees doing the registration should sign. The foreigner should keep one copy of this print-out, for their records.

People who were registered to vote in 2009 or 2013 will still be in the system, but should approach a change-of-address booth or a CNE office if any of their personal details have changed.

For more details, you can check the official memorandum (PDF).