I was participating in a Silhouette match and a thunderstorm quickly blew by. At one point the rain was coming in sideways and it reached my rifle which was 15 feet from the edge of the cover.

I didn't think much of it at first until I noticed a small "bump" on my vertical crosshair which soon turned into a series of mildots. By the time of the next relay the scope was completely fogged over. That has disappeared but there are still droplets of water on the interior lenses. I would guess if the scope was nitrogen filled it had long ago leaked out if it lets water in.

I love the scope but what do I do to dry it out?

Ooops, forgot to mention this is one of the old Weaver T's, steel tube probably 20-30 years old.

With a period scope like that, I think I'd put it in the oven set at the lowest setting, like 150 degrees to see if it dries out.
If not, and you must have it repaired, then IIRC Iron Sight in Tulsa, OK now does the vintage Weaver work.
Here's their info. I have no expaerience with them other than I know they bought all of the repair parts from the guy in El Paso when he quit repairing old Weavers.

Iron Sight Inc Redfield/Weaver (El Paso Scopes)
4814 South Elwood Ave
Tulsa, OK 74107
918-445-2001 or 918-521-7736
http://www.ironsightinc.com/

I don't think it ever had nitrogen in it. It certainly isn't waterproof anymore. On the Weaver steel fixed power scopes, the reticle should be just forward of the eyepiece. You can unscrew it and let it air dry. If you want it purged with Nitrogen, you will have to send it to Iron Sight.