"Puddle"? Sounds a bit more than a puddle...
Petrol or diesel?
You may be lucky, and it's just a bit of water in the high tension (spark) system of a petrol engine. This may just need taking the distributor cap off (the thing all the spark leads go to), wiping it thoroughly dry and replacing it (making sure the spark leads are not muddled up). Also worth cleaning and drying the ignition coil (the thing on the other end of the central distributor lead) and the spark leads themselves. This often stops a petrol engine when driving through puddles too fast, as the water splashes up inside the engine compartment, and water does not go well with high voltage.
On the other hand, if the air intake went under (in whichever kind of engine), it will have sucked water -- though this does take some depth. In this case you may be talking serious damage. If water got as far as the cylinders, the pistons will have hit a solid wall of incompressible water, and you will have bent con rods and who knows what. Could be a new engine or worse.
The other problem is that water may have got in to the wiring loom and other electrics, especially if the car was standing in deep water for some time. Also water may have gone in through the exhaust while the engine was stopped. Definitely a garage job.