Once you have registered for an account you can login by going to https://reloading.slack.com
You should see a page that is similar to this:
Enter your email address and password, and then you will be taken to the Slack site where all of the magic happens.
Be sure to take the time to configure your account. Details can be found here: How to configure Slack
Slack will work just fine from a desktop browser, but if you desire, they also make apps for Windows, Macs, and Linux OSs.