You shouldn't need a new fork to do this. If you mean you need to replace it for some other reason, then the main thing to look at is the steer tube. Usually they are 1" threaded or 1 1/8" threadless, although 1" threadless and 1 1/8" threaded do exist too. Also the steer tube has to be long enough for the frame. Other than that, you have to see if the fork will fit the wheel and tire you want to use, as well as the type of brake you want to use.

The geometry of the fork is important too, though I'm sure someone else can explain that better than me. I have done a fork swap with something that had different geometry, and it changed the handling of the bike quite a bit, luckily in a good way. A touring fork generally is meant for 700c wheels, while most MTBs come with 26". If it doesn't have cantilever brake mounts, it could work if you track down a caliper brake with long enough reach, but I'm not really sure if it would work well. I'd just find a rigid MTB fork to use though, easy, cheap, and as long as the steerer is right, should work without much issue.

For drop bars, you need different shifters, brake levers, and probably a different stem. If you have cantilever brakes, most road levers will work fine, if you have V-Brakes, you need travel agents, or special brake levers. Usually you will want a stem that brings the bars higher and/or closer to you.

I just put the finishing touches on my Schwinn Mirada conversion, 1.5" Kenda Kwest slicks (Might go back to 2.0 Big Apples, not sure), Cyclocross levers, and Suntour Command shifters. It's not exactly lightweight, but this bike is amazing to ride. Yes, that is a lot of seatpost, and yes, that is a lot of saddle to bar drop.