Squish... Squeak.... Squish... Squeak...
The noise is uncomplimentary, not just for yourself, but for others as well. Plus, you don't want to be caught wearing such shoes. Although getting wet is one of the reasons why shoes can become squeaky, there are often times when new shoes (mostly leather), can act up like this. At such times, there are a few techniques you can use to avoid the unwanted attention.
Tip #1 - Glue
If your shoes are new and there's no way that water could be the reason behind the noise, then perhaps the heel of the shoe is loose. To fix it, apply a little bit of glue on the inside of the sole. Press on the sole and hold it for some time. Once the glue has dried, wear the shoes and walk in them to check whether the noise persists.
Tip #2 - Hand Lotion
If the first tip doesn't work and you still want to know how you can make your shoes not make the noise, apply some hand lotion inside the shoes.
Tip #3 - Sunlight
When shoes get wet in the rain or otherwise, keep them out in the sun to dry for at least 2―3 days. If water is the culprit, the heat should help and give your shoes its previous glory. Touch the insoles and around the shoes to check if they aren't damp, before you wear them again.
Tip #4 - Cornstarch
Sometimes, the inner soles of the shoes are not completely glued in, and can be removed with ease. If you can do that, then take out the inner soles, apply some baby powder or cornstarch in the area. Place the soles back in their places, and keep the shoes aside for the night.
Tip #5 - Saddle Soap
As a last resort, you can check to see if the tongue of the shoes aren't rubbing against the shoes; it will be under the laces. And if it is so, apply saddle soap on the tongue, rub into it, and then wear the shoes to check if the noise is there or not.
Squishing, squeaking shoes are annoying and can definitely be frustrating. Your first task should be to find the cause, and apply the right solution immediately. And if none of the tips mentioned above work, you can try to return the shoes (if you've just bought them). You can explain your issue with the shoes, and ask if they can be replaced.