Currently OnePass Gold and Platinum members may upgrade one companion (assuming space) at the airport for any CO or CM (Copa) flight that is not operated as BusinessFirst. The upgrades are not done in advance and are cleared at the gate.

You will have to speak to an agent about ensuring your companion is on the upgrade list as this is not something that is done automatically nor is it something you can do yourself.

Companions are listed with status of the elite sponsor (e.g. if you’re a gold and list you significant other for an upgrade, s/he will be prioritized with the golds). Companions clear after all other non-companion elites within their group have cleared.

For example if a Platinum companion, two golds and one gold companion are standing by for an upgrade and only three seats are vacant, the platinum companion and both the golds will be cleared into F and the gold companion will not clear.

The official rules state that the companion "traveling on the same itinerary" as the elite member is eligible. In reality, this just means on the same flight. You do not need to be on the same PNR (and probably don't want to be, as noted below) and can actually be flying different overall routings. As long as you are on that one flight together you can request the companion upgrade. For example, passenger A travelling DCA-CLE-LAX-CLE-DCA can request that passenger B travelling CLE-LAX-CLE be added as a companion for both the CLE-LAX and LAX-CLE segments.

One final note: having multiple people in a PNR will have a negative affect on EUA's but will not impact airport upgrade chances (aka battlefield upgrades).

In order to have the best chance of getting the companion upgrade ask EVERY GA/TA/PC rep you deal with on your day of travel to add the companion to the list until it is done. This is especially important for downline flights and less of an issue with a flight originating at the station you're talking to the employees at. Basically you do want to be on the list as early as possible - and you will likely see the place in line on the waitlist improve as the agent does their magic. There is no longer a "2 hour" rule that requires you to be within 2 hours of departure to add someone to the list. Nor is there a requirement that you be at the departure airport. It is, however, required that the companion be checked in for the flight.

If the agent gives you gruff about the person being already on the list politely remind them that as a companion the status will be significantly improved (assuming your elite status is higher than your companion's). And if they insist on being an arse about it move on to the next agent.

Review of how to tell if your flight is market as a BF

EUA upgrade hierarchy
Airport upgrade (aka battlefield upgrade) hierarchy