I just went through this myself. It isn't difficult, but it is critical to mate the parts exactly. Get all the glue off. I was able to just scrape to get to bare wood on the bridge. The top might be a different story it the wood from the top was torn off. Is it has been damaged it might be necessary to sand or scrape into a larger area of the top, thus requiring refinishing, to get it smooth. Once the top is smooth, work the bridge shape until it fits. A good test is a strong light under the bridge, another is to use chalk between to surfaces to find the gaps. After they match you should be able to apply very light pressure (a few ounces) and not be able to slide a 0.001" feeler gauge under it.
With the bridge dry fitted, mask it off with tape. I use Titebond for this join. Use a credit card to squeege glue on the top. The tape thickness is a good thickness for the squeeze out. Squeege glue on the bridge. The goal of applying glue completely to both surfaces is to 1. Fill all wood pores with glue, and 2. To ensure the is no air trapped in the joint. Side note, trapped air in a glue joint is a major cause of failure.
Let the glue tack for about 90 seconds. This stops the peices from sliding. Drop on the bridge, give it a slight wiggle to smear the joint. Drop in the locating pins. Apply light pressure. If the parts mate well you will only need about 5 lbs over the entire bridge, maybe 1 psi. Long bridge clamps are not necessary.
You should get a small amount of even squeeze out. But wait about 2 hours to clean it. It is a much easier job to scrape dry, but not too dry, glue than to wipe up wet glue and have it smear. Most of the squeeze out should be on the tape anyway.
Wait a solid 24 hours before putting the strings back on.