For the services:
In the admin section, you can choose which social network icons/buttons you want to display. You can also set the order of the icons/buttons to display. If you do not want to show and icon, click on the open/close icon and disable the icon. Enabled icons will be shown in blue and disabled will be in red. Be sure to select the update button after making any changes.

Where the buttons are shown is controlled by the theme and it’s template files. You can delete or comment out the lines that show the buttons in each of the template files.

Take a look art the codex article here. http://codex.simple-press.com/codex/plugins/our-plugins/available-plugins/plugin-share-this/

I shows where you can put the displays and that is the approximate places you will find them in the various template files in the theme.

You should, of course, create a custom theme before you start editing so you don’t lose any changes when updates come out.

Hmmm. OK, that’s more work than I want to do right now.

I tried selecting “small icons,” but it doesn’t actually end up looking like the picture. Instead, it has the small icon AND the text name (facebook, tweet, etc.) next to all the icons (except g+1 for some reason).

I’m using large icons now (they display correctly), but I’d really prefer the small icons without the text. Help?

there are five options for images… large icons (no text), small icons (no text), buttons (text), horizontal counts (text) and vertical counts (text)…  the first two have no text…