Welcome to FT, DMBmelch!

Since you're flying Continental (CO), your best bet would to look at their program for upgrades. While it's possible to upgrade a CO flight using miles from other airlines, you would need to have booked a very expensive B or Y fare.

The cost of your upgrade on CO depends on the fare basis of your ticket. The mileage is the same for all fares - 30,000 (unless you have a Y fare where it's only 15,000) - but there is a co-pay that depends on the fare. The co-pays are
If you decide you want to try for the upgrade, your mission, should you choose to accept it, is to accumulate the miles you need as quickly as possible.