WORKING WITH YOUR LAYERS
One of the main difference with PSP and Photoshop is the way they handle layers.
When working in Photoshop, you may drag a layer directly from the layers pallet onto another canvas just as in Paint Shop Pro.
But the select and copy function is just a little bit different.
When copying a layer by copy and paste you should first Select > All from the top menu in your screen.
Now Edit > Copy (or CTRL + C on your keyboard)
When going back to your other document, take care that you do not click on the canvas, but rather on the top bar of the document. Otherwise you will activate the tool you have in use at the time.
Edit > Paste (or CTRL + V on your keyboard)
This will paste your image as a new layer directly above the layer that you have highlighted in your layers pallet.
You can also use the Move tool to directly move the image from one canvas and drag it onto another.
To move the layer up or down on your canvas, just drag and drop in the layers pallet to the order you want. Just the same as in PSP.
RESIZING A LAYER

I have noticed that there is a lot of confusion as to how to resize a layer in Photoshop without having to resize the whole image. To do this, you will need to go to Edit > Free Transform. Then you will notice a box around your layer that has a center point and a point at each of the four corners / sides. All you need to do is drag the points around to the size you want it to be.

There are also value boxes at the top of the screen. There you will notice a chain between the H (height) and W (width) values. Click this chain to turn on the aspect ratio option.
After you have your layer the size you want it, either click the check mark at the top of your screen or double click inside the bounding box on your image.
LAYER STYLES

I know that PSP has now incorporated somewhat the layer styles like Photoshop has. (or so I read) So now I will show you how to use those styles in Photoshop.
To bring up your Layer styles, you may either double click the layer (OFF of the name, otherwise you will rename the layer) OR you may right click the layer and choose Blending Options OR you may click the Layer Styles button at the bottom of your layers pallet.
Each of the options are pretty self explanatory. Each tutorial will show you which to use and where. Eventually, you will be able to create your own styles.