Making perfect selections is difficult no matter what tool you use: the magnetic lasso, the magic wand, the quick selection tool, and many others, which is why the Quick Mask is your friend.
Just know up front that "Quick" is a cruel misuse of an adjective meant to taunt you as you painstakingly refine your selection. Best to overestimate how much work it will be to make a good selection, then you can be happy if it doesn't take too long.
Now that I've crushed your optimism, let's move on to a very basic look at the Quick Mask. The quick mask is a nifty red semi-opaque overlay (by default, change color or opacity by double clicking the quick mask icon) that lets you see what you have selected and allows you to make and refine selections. The quick mask tool icon is hiding down there at the bottom of the toolbar:
Or you can find it in the select menu:
Here is a typical way that you might use the quick mask. Let's say that you want to isolate some element of a photo from its background. In this case, let's say I want to take an ornamental ironwork detail, extract it from its background, and save it to use as part of my own brush set or for some compositing project.
For the sake of demonstrating how the quick mask can be used to refine a selection, I will make a really sloppy initial selection with the magnetic lasso tool:
Your selection would never be this bad, but I want to show you that even if it is, you can fix it in a very intuitive coloring-book sort of way. Without deselecting anything, hit "q" to enter quick mask mode (or select it from the toolbar or menu). The red mask lets you see which areas are selected and which are not.
Now that you're in quick mask mode, you can use the paint brush (or pencil or selection tools, but we'll stick with the paint brush here) to refine your selection. Hit "b" to get your brush. As you paint, you can increase and decrease the brush size as needed with the right (bigger) and left (smaller) bracket tools. You can adjust the hardness of the brush (for harder or softer edges) by holding shift while using the right (harder) and left (softer) bracket tools. You can hit "x" to toggle between black or white (i.e. masking or unmasking). Finally, you can toggle between quick mask mode and your selection (the "dancing ants") by hitting "q", but be careful not to click on the image (and accidentally deselect) when you're not in quick mask mode.
It's simple, but it takes time. Things that help: a steady hand, painting or drawing experience, a pen tablet, a zen-like mindset. Sadly, I have, at most, only two of those things.
A detail (above) shows the area that I am painting (with a black brush).
As I work, I hit "q" to check how the selection is progressing. Still work to be done...
I gradually work around the whole thing. Here's the improved version in quick mask mode:
And here is what it looks like when I hit "q" again to turn off the quick mask and go back to my selection.
It's still not perfect, but I have a movie to catch. Priorities. So with my selection still active, I copy it onto its own layer (Mac: Command–J; PC: Ctrl–J):
As you can see, there are still some parts with too much black around the edges. From here, I can use the erase tool to clean it up. If you do a better job up front than I did here, you might already be done.
If you have never used quick mask, just experiment with it (preferably on something with clean edges). Have fun. More work on selections/masking/compositing to come.