Write a letter to (for example) United's Mileage Plus and advise them you would like to start using their airline more but it's difficult to make the switch without the perks associated with your Gold status at Delta.
Enclose a copy of your latest Delta SkyMiles statement (a copy of your on-line statement might suffice, particularly if you print enough to show an active history) which shows your Gold status. Ask for comparable status. The entire letter should be no more than a half page. Be sure to include your Mileage Plus number!
I have tried this four times. I'm four for four.
Your new status will normally be valid for the rest of the year. You will have to earn the Gold status on United to be treated as such next year. A similar letter sent for next year normally won't work.