Some helpful tips for using the Photoshop Eyedropper…
First, if you're using a tool that involves a color (paint brush, paint bucket, vector shape tool, etc.), you can hold down the Alt button (Option for Mac) and the cursor will change into the eyedropper, allowing you to select colors from your document. This is very useful for me as I'm lazy and would rather limit how often I switch tools.
Another tip is that you aren't limited to the colors in your document when you're using the eyedropper tool! You can pick colors from other visible documents, from the Photoshop interface—even from other applications as long as you can see them on the screen! As long as you start in your document and click-and-hold with the eyedropper tool, you can then drag outside of the document to anywhere in your window and pick a color.
Finally—if you're like me (not overly observant or very task-focused), you may have never even noticed the toolbar options area. The "sample size" dropdown allows you to use the eyedropper to gather a "point sample," a 3×3 average sample, or a 5×5 average sample. This is really useful if you have an image that has a lot of shading going on, and you want to get an approximate "average sample" instead of a weird color from a particular point.