How can I teach our kid to get rid of old toys and play with what he need and keep the rest in a box?
In regard to the first question: The easiest way to do this is probably to buy an "old toys" box and sort through the playthings together with the child. The kid decides what goes in the box to fill it; you decide how big the box is. Then move the box to the basement/attic/garage/other-out-of-sight-place. This way, the toys aren't gone yet; there is still a chance they can be reclaimed when the kid needs them again.
Once the "old toys" box has been sitting in the basement for a few months, it might be easier to go through it (again, with the child) and decide together what is really no longer needed. But be prepared for a lot of disagreement in that regard.
As to your second question (how to keep the "active toys" neatly in a box): I wish I knew the answer to that. This is one of our greatest sources of disagreement and conflict in our family.
Our current solution is to have the kids clean up whatever they played with in the living room (and the rest of the rooms that we share) before they go to bed, because "the grown-ups live there too and want to use it in the evening". When they were younger, we did it together with them; now that they're school-age, they do it by themselves (but, unfortunately, never without us first requesting they do it, and almost never without bickering among themselves about who is doing less than his/her fair share). We don't care as much about the kids' rooms; they have to clean them up so they can be vacuumed etc, but that doesn't have to be every day. I really dislike living in a mess, and I'm having trouble with the state of chaos that my kid's rooms are usually in, but then again, it's their rooms.
In fact, I think your sense of how much order is "right" may change as you get older: I used to never understand my parents when they forced me to clean up my room, but now the disorder in my kids' rooms (which probably isn't much worse than what I had in my room) is really bothering me.
So my current position on the question of a neat and tidy house is that the price of having kids is to live in surroundings that sometimes look as if a bomb had exploded in them. I'm hoping that this state of affairs will gradually change as the children get older and toys and picture books lose their attraction, but I've mostly lost the will to enforce a state of order in which I would feel comfortable. The energy and the arguing required to achieve this goal, along with all the bad feelings created in the process, are simply not worth it to me any more.