If you run Wordpress on a localhost using WAMP server and your custom permlinks doesn't work, try this quick fix.

Step 1: Click on the Wamp Server little icon on your PC's right bottom corner.

Step 2: Select Apache, Apache modules.

Step 3: Click to enable rewrite_module.

That's all to it for the short story and you're good to go.

Keep reading if you're interested to know what happened, here goes
WAMP server's default installation does not have Apache rewrite_module enable, hence when you select Custom URL in Wordpress it does not understand the new rules written in your htaccess file that control your URL's new structure.

Well, if you're really into the techincal stuffs, here is a link that explained in full what really happened: What rewrite_module in Apache means

Related post:
How to start your Wampserver

How to install a web server on PC which basically show you how to install Wampserver on a PC for their work from home projects.