Yes selenium can be used to automate the manual interaction steps.
It's intended to be used against web browsers and it's widely used and implemented.
However this is only half of the puzzle. Selenium is the core technology in browser automation tools, APIs and frameworks. To actually USE selenium you are going to need to pick an actual implementation.
You can start of with the IDE plug-in for Firefox. This is nearly always referred to as a quick and dirty, temporary solution. It does not need to be. If you use it to record existing interactions and try and play them back, or do selections based on text, then yes, the test suites you create will be brittle. If you use good practices such as css ID's and HTML data-attributes you can create robust and complex automation this way.
It also has the benefit of actually letting you, or even your product team, see the automation for themselves.
It has the downside of only running in the browser IDE that it is implemented which I believe is still just Firefox so starting it is still a manual step.
The other, more extensive and maintainable options is to use Selenium from within test framework such as Ruby On Rails with Rspec and Capybara which enable you to write scripts which can be run headless and against different browsers. This approach has the downside of not showing you the actual screens which might have visual layout issues.
Programming Languages & Frameworks
Languages are supported through drivers with commands from the Selenium API as methods/functions.
Testing frameworks that can be used with Selenium:
C# - Frameworks: NUnit Haskell
Java - Frameworks: JUnit, TestNG
PHP - Frameworks: Behat + Mink, Yii
Python - Frameworks: unittest, pyunit, py.test, robot framework
Ruby - Frameworks: RSpec, Test::Unit
How can you write tests for Selenium (or similar) which don't fail because of minor or cosmetic changes?
Selenium and non technical team members
and in convincing the business to support:
What problem does automated user interface testing solve?