How can I secure passwords stored inside web.config?

Generally, web.config is a secure file and IIS does not serve it, therefore it will not be exposed to users who are making requests to web server. Web server only serves specific type of files and web.config is surely not one of 'em.

Quite often you save your database connection string in it which includes password. Now imagine an scenario where web.config was not secure. You have created a major security threat to your application.

Therefore, specially as long as your project is not too big, you should not be worrying about it.

Yet, you may have a better approach but creating a project called "Resources" and save all the critical information such as settings, consts, enums and etc in there. That would be a slick and organized approach.

If you are passing the username/password over the wire though (for example in case of a secured API call), you may want to use https to make sure that information that are travelling are encrypted but that has nothing to do with the security of web.config file.

You can encrypt the web.config with aspnet_regiis. This is to stop people with access to your server from reading sensitive information.

By the way, I would put your config settings inside a class, that can then be injected into your controllers - it will make unit testing easier.