I thought I was "cleaning up" my computer but apparently deleted Internet Explorer. Is there a way to re-install it?

That was a very thorough "cleaning". The current version is available at Get Internet Explorer 7.

Open 'My Computer' and type in the URL like you would do with Internet Explorer. The menu bars will adjust themselves to become Internet Explorer.

Let us encourage you to take this opportunity to IMPROVE your web experience by installing Mozilla FireFox instead. I ignored this suggestion from people for two years, did it during an upgrade last year and can't BELIEVE how much better/secure FireFox is over IE.

Give it a try.

Firefox web browser | Faster, more secure, & customizable

FireFox Addons - Powerfully customize your new browser

As he suggested get Firefox cause it's way better and more easily configurable but you should reinstall internet explorer because not having in installed could cause windows update to malfunction

Every once and a while I have to use IE or the IE tab in Firefox because Firefox won't work with the particular website.

FF is overrated. I do use it for most of my browsing, but some sites fail to work with FF.
Also as a webdesigner, I often see MIE displays CSS correctly much more often then FF.

FireFox still needs some tuning to really become best.