How do you know timing belt snapped?

There are two things to consider here. First, where is the camshaft located in your engine, and second, is it an interference setup. If you don't know what either of these things mean you should take the car in and have it repaired. Nothing personal, but it takes years of training and experience to be any good at this.

Every stock in-block cam engine I've ever worked has not been interference, which means there's no valve damage if the chain or belt breaks. So you can simply follow the repair procedure and replace the timing components.

On an overhead valve engine that is not interference, again the timing belt or chain can be replaced - there shouldn't be any other damage.

Now the fun part. If it is an interference engine and the engine was running when the belt or chain failed, it will likely need a few valves if not a cylinder head. You can determine if there was damage by a visual inspection or by performing a leakdown test on each cylinder with the camshaft bearing caps loosened and the valves closed. Obviously any damaged parts have to be replaced. If there was damage to any valves it is also important to measure the piston to deck height on each cylinder. It is possible to bend a connecting rod when the piston contacts a valve, especially if the valve head broke off and jammed in the cylinder (this also usually makes a nice crater in the piston). I've seen cylinder heads replaced where the tech neglected to take this measurement. It was only a matter of a couple hundred miles before the damaged connecting rod let go and caused catastrophic engine damage.