Shoes are a runner’s most important tool, and keeping your shoes dry in between runs is one of the easiest ways to prolong the life of your running shoes. Obviously, you should feel free to get them as wet as necessary while you are out running and having a good time!
When your feet are not in your shoes, though, you should keep them as dry as possible. That will prolong the life of the shoes, as well as prevent you from hurting yourself or getting blisters when you put them back on.
You have to be careful about how you keep your shoes dry, though. Never put your shoes next to a heater or in direct sunlight, which can damage the shoes even easier than leaving them wet by degrading the rubber. Instead, always make sure that your shoes are at least a few feet away from the heat source, preferably not outside in the sun or right underneath a window where a lot of sunlight comes in.
A good way to allow your shoes to dry faster is to pull the insoles out of the shoe when you are not wearing them. If you pull the insoles out so that just the ball of the foot is sticking inside of the shoe it will be easier that to keeps the appropriate insoles with the correct shoes. That will also make it faster for you to put the shoe back together before wearing it.
Removing the insole will allow air to circulate within the shoe, which will speed up drying time. This will only take you a few moments at the end of a run and a few moments before going out for a run to accomplish, and can really speed up the safe drying of your shoes by quite a margin.
Another way to speed up the drying of your shoes is to get them up off of the floor. If you put your shoes on a rack, more air can get under the shoes and you can allow your wet shoes to drip onto the floor rather than having any water that might drip staying in contact with the fabric of your shoes. I recommend putting the wetter shoes closer to the floor than your dry shoes so that you can keep them dry. As you wear the dry shoes out in the rain and puddles, you can move your previously wet shoes higher up the rack to replace with your newly wet shoes.
For extremely wet running shoes there are two very effective methods that you can additionally use to dry them quickly.
The first thing that you can do, and the most effective, is to put your shoes in front of a fan. This will make sure that you have dry air constantly moving past your shoes, which will help the moisture trapped in your shoes evaporate and be carried away by the air your fan is moving over them. This is the safest way to dry your shoes, and works especially well when you place your shoes on a rack.
The second thing that you can do is to wad up some newspaper and stuff the toes of your shoes with them. This will not hurt your shoes, although the ink can seep off of the newspaper page and stain the inside of your shoes if you leave them in there for too long. Stuffing the shoes with newspaper can speed the process up by absorbing the moisture from the shoe and into the paper. Just be sure that you remove or replace the newspaper quickly and regularly.