This was all in the tutorial, but here's a refresher: You get shares by selling your company. Based on your company level you need a certain amount of progress in order to sell your company. (goes up every level, caps at 5000) Your progress is the green circle that fills up around your level indicator in the upper right circle. (to the left of the door that takes you to your private office) You can also click on the indicator to see the actual numeric value of progress vs. what you need.
Progress is directly equal to the combined number of levels of your employee girls. When you have enough progress to sell, the green circle will be full (obviously) and the border around your money/income per second will turn from gold to green. You can then click the indicator and choose whether to sell straight out, or double your shares by spending 50 gems. When you sell you get base shares equal to your progress, + whatever modifiers either from the decoration somebody else mentioned, or by spending the 50 gems to double them.
Then you start "over" to build up your company at the new level.