Sirex & Rory have covered getting them out of the water pretty well, but given that getting them out of the water in the first place might be no small feat, you're right in understanding that you're far from out-of-the-woods, so to speak, even after they're out. Getting the victim warmed up is paramount, and their wet clothes are going to be a serious impediment. If there's any way to get them out of their wet clothes and into some dry clothes, that's pretty high on your list. Some possibilities:
- Get dry clothes from someone's backpack (maybe the best option).
- Borrow clothes from someone else (ie, strip off the wet clothes and take someone else's jacket, etc.). This, of course, now gives you two people who aren't properly dressed, so you really want to accelerate efforts to get the whole group to safety. Since this puts another person at risk, you'd want to be pretty cautious about employing it.
The whole idea of changing clothes is that your hiker will be lots more likely to be able to warm himself back up in dry clothes than in wet clothes, so you're looking for any reasonable option to help that happen.
Next, you need to assess your status and consider getting the whole group to safety as soon as possible. If you've been able to get your soggy hiker into some dry clothes (fully or partially), you may be able to just continue your hike. You'll generate some body heat by moving, which will help some. If you have a short distance to travel in order to reach shelter / warmth, this is probably your best bet.
If, however, it's cold enough that you're not going to warm up by hiking, or if you don't have dry clothes, or you had to borrow some clothes from someone (leaving two or more hikers under-dressed) I'd strongly consider getting a fire started in order to warm up and dry off. Some sort of reflective surface (tarp, rock wall, etc.) may help warm you a little more evenly. Dry out your clothes, but don't burn them!
Keep an eye on time vs. your itinerary. If stopping to build a fire will cause you to not be off the trail by nightfall, you'll need to decide if you're staying put overnight or sending someone out for help. All the usual wilderness first-aid guidelines apply here -- don't send anyone anywhere alone, and a group of four is a great deal better than a group of two or three. If you don't have a large enough group to send a capable party for help, I'd be inclined to stay put and keep the group together.
The whole idea here is to keep your head and use the resources of the group to avoid making the situation worse while you're trying to recover.