Your images will be something like jpg but once you start editing them they will become PhotoShop Documents [psd].
You will have to export them back to the format you want.
First of all NEVER work on your original image. Always make a copy and work on that. I've saved to the wrong format and over written files too many times for it to be funny any more.
Photoshop layers as I know them...
If you select an area of an image and copy and paste in to the same image, Photoshop will add it as a new layer automatically and it will be the new top layer. The same is true if you add an object or text.
This is were it starts to get difficult to explain....
Layers are like the old animators acetate sheets. You can draw on one layer without affecting the others, but you can see the whole image at once. You can also turn off [remove but not delete] layers if you want to see something on a lower layer. In Photoshop you should be able to see a pane/window on the right of your screen that shows you how many layers you have and how they are stacked. You can move between layers by selecting in that pane and even move the order of the layers about by dragging and dropping in that window.
The Lasso tool lets you draw around something to select it. If you zoom in close enough you can select the outline of an object pixel by pixel. The Quick selection tool [just below it] does a similar thing but more quickly as it decides where the edges of your object should be. I'd try selecting, cutting a pasting until you get the hang of it. The trouble is that most objects do not neatly end at one pixel, they bleed or disappear over several, so there is a lot of skill in getting this right. Each time you make an object selection you can redefine the selection by changing it size [bigger or smaller] or feathering or smoothing the edges. These options are all available under the Select tab at the top of the Photoshop screen.
To keep the layers you will need to save the image as a Photoshop document [psd]. If you save it back as a jpg or png all the layers will be merged in to one.
I'd start on images that you don't care about... and work on copies of them. Have a play and see what happens.
Thing like colour changing can be relatively straightforward if you have good selections to work from.