Hi there - you can remove the author and date with this CSS code:
.postmetadata {
display: none;
}
Just head over to Appearance > Custom Design, and click on the CSS tab.
Copy-paste the above code into the CSS area, below the green block of comments, and save your settings. Voila!
If you need help with CSS tweaks in the future, feel free to post in our CSS Customization forum:
http://en.forums.wordpress.com/forum/css-customization
Here are some resources where you can start learning a few CSS basics - it can be really fun once you get started!
CSS Basics
Editing CSS
Custom CSS
Let me know how it goes!