There are a few outcomes that could happen when a bow is dry-fired, the first is that your bowstring, and cables could snap resulting in your limbs breaking and potential debris flying all over the place. This is basically the worst case scenario. The second scenario is that your string breaks however everything else stays intact, and the third possibility is that it will appear that nothing has happened to the bow.
No matter what scenario your bow falls into after being dry-fired, the first thing you will need to do is to get a magnifying glass and a bright light and look over the limbs especially near the cams for any cracking, or splintering. If you find that one of both limbs have cracks or splinters in them then you will have to replace the limbs before you are able to shoot again.
After checking for cracks and splinters in the limbs, take a look at the cams/wheels to make sure that they have not been bent or cracked, again if they are you will need to replace them as soon as possible before you are able to shoot. Next if you were lucky enough to have your string still intact, you will need to check the whole thing for badly frayed portions, cut strands, and badly damaged areas, especially near the axles.
If everything checks out and you were unable to find anything wrong with your bow then you are lucky, and you have 2 options, your first option is to draw the bow(with an arrow) and shoot it. Make note of any weird noises, or vibrations. If you aren’t the risky type then you can bring it into a bow repair shop and they will have the tools and resources to be able to better inspect it for damages.
In any of the other cases where the string breaks and/or the bow limbs shatter, you will first go get medical attention if you need it and then you will need to bring your bow in to a bow repair shop and you will have to replace the limbs,string, and any other broken parts(axles,cams,wheels etc.).