Nikon D3000 doesn't have a live view which means that the scene can't be seen on the LCD screen.
So, how do you use the manual focus in such cases? Hit and trial, or is there a way out?
You still use the autofocus points most of the time. Even though the camera isn't doing the focusing, it can still tell you when things are in focus, and the green focus indicator light in the viewfinder will come on when the image hitting the selected control point is in focus.
If you work mostly in manual focus mode, it may be worthwhile getting a new focusing screen with the kind of prism-collar and split-image focus aids we used to use in the pre-AF days. That can be an expensive option, though, especially when compared to the D3000. If it's important, go for it, but it can make the viewfinder block out in the center when you're using slower lenses, and you probably have higher priorities for additional investment in your gear.
You can sort of focus by eye on the ground glass, but because of the focusing screen's design, it is hard to be accurate at all -- it's something best left for small-aperture, large depth-of-field shots where focus errors won't show very much.
+1 for using the focus lock green light
It's hard to judge when you have the subject focused just perfectly. But if you rock the focus back and forth, so that you're focusing in front of, then behind the subject, it can help to find that place in the middle where focus is right on your subject.
If you are using the centre focus point, you can always focus until the green light comes on, then recompose your shot.
After buying a few old Nikon prime lenses for my DSLR, a D5500, I found that I REALLY missed the Split Focusing Screen found on old film cameras. Luckily a Google search revealed that one could "easily" be added. I decided to give it a try and it is wonderful.