JVM garbage collection in young generation

It comes from Java SE 6 HotSpot[tm] Virtual Machine Garbage Collection Tuning , one stop place to learn everything about GC internals. But to address your immediate questions:

Allocating new objects using new operator (almost) always happens in Eden space. But Eden is actually a stack. When you create new object needing N bytes, single pointer advances by N bytes on that stack and that's it. Allocating is that fast, no searching for free spot, compacting, whatever.

Of course this stack is not infinite, at some point we'll reach its end, triggering minor GC. Also most likely multiple objects are already garbage. So what JVM does in minor GC is the following:
traverse graph of objects starting from GC roots

copy all objects reachable from GC roots to one of survivor spaces (no gaps, we know all of them and this is a single process)

wipe out eden space (basically just moving this stack pointer back to 0)

In subsequent minor collections there are additional steps:
one of survivor spaces is examined as well. Live objects from both eden and one of survivor spaces are copied to second survivor space. This means there is always exactly one free survivor space.

So how are objects ending in tenured generation? First young objects are copied to one of survivor spaces. Then they are copied to the other and again and again. Once given object jumps back and forth too many times (configurable, 8 by default), it is promoted to tenured space.