Since you are using Wamp, it means you didn't install and configure, Apache, PHP and MySql on your own, but downloaded bundled versions with installer. My recommendation is that you download and use Bitnami Redmine from https://bitnami.com/stack/redmine/installer
However if you want manual installation, you already have Mysql with WAMP, so you just need to install Ruby and Redmine.
- Choose appropriate ruby
For Windows installations, you must first install Ruby, check Redmine and Ruby compatibility matrix for Redmine from:
http://www.redmine.org/projects/redmine/wiki/RedmineInstall
- Then download Ruby from: https://rubyinstaller.org/ and I also recommend DevKit, nowadays there are bundled versions, on downloads section.
- Follow the rest of installation instructions from link provided in step 1.
- Run Redmine from Windows console, using rails s and you can access it from browser via port http://localhost:3000
To use Redmine API, you must first enable it, via Administration | Settings | API
That's it!