Step 1: Using the Ellipse Tool, draw out a circle. Hold down SHIFT on your keyboard to make the circle proportional. Choose any color for the fill - You don't need a stroke color.

Step 2: Using the Rectangle Tool, draw out a rectangle making sure it overlaps the circle. To help you with lining the shapes up while drawing, make sure the Smart Guides are on. To do this, go to View > Smart Guides and make sure it's selected.

Step 3: Now let's merge the shapes together. Using the Selection Tool select both shapes, holding down SHIFT to select multiple shapes. Go to Window > Pathfinder to open up your Pathfinder palette. While holding ALT (OPT on the mac) click on the "Add to shape area" option.

  

Step 4: We have the bottom half of the pill done. Let's create the top half now. Select your bottom half with the Selection Tool and then go to Object > Transform > Reflect. Choose "Horizontal" and then click "Copy". A second shape was just created. You want to move this shape up so that it meets up nicely with the bottom half of the pill. I filled the top half of the pill with white and no stroke color.

Step 5: Because we're going to make these shapes 3D using the Revolve feature, we only need half of each of them. So using the Rectangle Tool draw out a rectangle over the two shapes. We'll use this to cut the shapes in half.

Step 6: Before we cut away from the shapes we need to keep a copy of the rectangle shape in memory. You'll see why in a second. So make sure the rectangle shape is selected and go to Edit > Copy or hit CTRL + C. Now using the Selection Tool select the rectangle and bottom shape (hold down SHIFT to select multiple shapes). Go to Window > Pathfinder to open up your Pathfinder palette (if it isn't already opened from before). While holding ALT, click on the "Subtract from shape area" option.

Step 7: Notice that the rectangle shape is now gone? We still need it though to do the same thing to the top shape. That's why we made a copy of it. So go to Edit > Paste in Front and the rectangle is available again. Using the Selection Tool, select the rectangle and top shape. Hold down SHIFT to select multiple shapes. While holding ALT, click on the "Subtract from shape area" option on your Pathfinder palette. I then selected both shapes and grouped them together - You can do this by going to Object > Group or hitting CTRL+G.

Click on the "Map Art" option. The first thing to do is choose which surface area of the pill you want it to appear on. I chose surface area 5 and then selected my logo from the drop down box:

Then position your logo where you want it. You can also select to shade your logo by checking the "Shade Artwork" option:

And there you have it, the pill to cure all of your design headaches! Here is my final result: