Arrive at the airport earlier than you would need to otherwise. This will give you time to work on getting a free upgrade without feeling stressed or needing to rush to make your flight.
Check in at the counter instead of using a machine. This will give you the opportunity to actually speak to an airline representative about the upgrade.
Ask about the possibility of a free upgrade as you are checking in. Be polite and undemanding when you ask. If you have any special circumstances (such as being on your honeymoon), mention this as you are checking in. If you are lucky, the agent will upgrade you there. If not, don't lose hope.
Go through security and find your gate. Speak to the agent or agents there and politely ask again for an upgrade. As with the check-in agent, explain any special circumstances that would warrant an upgrade. If this does not work, and you are flexible, tell the agent that if the flight is overbooked you're willing to take the next flight in exchange for an upgrade.
