You might want to check out
http://www.continental.com/onepass/elite/upgrades.asp - it gives a rundown of the Elite upgrade process.
In a nutshell, Platinums will be upgraded automatically from all fares (except Priceline/Hotwire and mileage redemption tickets) if upgrade seats are available within 5 calendar days of the flight - it is not necessary call reservations to request the upgrade. Upgrade-eligible flights include:
All flights on Continental and Northwest within and between the lower 48 US, Alaska, Canada, Central America, the Caribbean, and South America*;
All flights on Continental Micronesia within and between Asia the Mid-Pacific*;
All Copa Airlines flights systemwide.
*Elite Upgrades not applicable to flights operated and sold with a Continental BusinessFirst or Northwest World Business Class cabin.
You may also upgrade one companion traveling with you once you get to the airport.