How to use a magnify/ amplify effect?

You can use any selection tool that does a good job of selecting the shape you need, then scale that. Below is a demo and you can see that it can take just a few seconds.

The steps:

1. Use an appropriate selection tool. I wanted a circle, so I picked the Elliptical Marquee tool, but first I showed you all of the selection tools that are available in case another selection tool would work better for your design or subject. 

2. Choose Layer > New > Layer via Copy. This copies the selection. 

3. Choose Edit > Free Transform (or Edit > Transform > Scale), and drag a corner handle to enlarge the new layer copy. 

4. Add any effects such as layer styles. I added a black stroke. 

There isn't a purpose-built tool as found in some other software (i.e. Snagit) to make a quick "magnified call out":

Create a rectangular or elliptical selection of the area and use Cmd/Ctrl + J to copy the selected area to a new layer, then optionally make it a smart object and then transform it larger, add layer style (stroke, drop shadow etc). One could possibly use the neural filter "Super Zoom" rather than the standard layer resizing methods. Here is a quick example, I used a vector for the stroke as it was better than a layer style: