I added the Events calendar that came with the DNN download. Is there a way to make it the size you want? I'd like to make mine a little smaller.

You'll need to look at themes for the module.   Several different themes are provided with the module, so you can choose one that suits you.  If none does, you will need to create a theme that works.

A theme is really a css file and perhaps some images needed by the css.  The best approach is to make a copy of the theme folder, giving it a new name, and editing the css.  If you know your way around css, this shouldn't be a huge task, and may require just changing a few classes.

I just added the "Events" module and it put a working calendar on the page. Do I need to do what you suggested to change the size of this calendar?

If you use the Edit Options dropdown for the module, you will be able to select which of the existing themes to use. You can see the variations that are available. Then, you can decide if you need to customize a theme. Note that one of the themes is a "small" one.

The 'small' calendar displayed, but wouldn't function at all. I tried the other types and there's one that will do what I need it to. When I view it by 'List View', it looks better to me and gives the same info.

Is there a way to change the color settings on the calendar and 'list view' bar?

You can change everything by editing the css.

If you need help with editing css, ask a few more questions and let us know what level of experience you have with css.

I know very little about css. Very little. I used Artisteer to create my skin and know that it used css in creating it. I don't know much about it at all though.

This tutorial may help you get started with identifying CSS classes, and provide you some tools:  Troubleshooting DotNetNuke Skins

Some other tutorials that might help include:

Beginners html guide for DotNetNuke
CSS Reference Book (112 page PDF)
Introduction to CSS and inheritance in DotNetNuke skins

If you google around, you will find some good tutorials on CSS.