How does copy_from_user from the Linux kernel work internally?
The implementation of copy_from_user() is highly dependent on the architecture.
On x86 and x86-64, it simply does a direct read from the userspace address and write to the kernelspace address, while temporarily disabling SMAP (Supervisor Mode Access Prevention) if it is configured. The tricky part of it is that the copy_from_user() code is placed into a special region so that the page fault handler can recognise when a fault occurs within it. A memory protection fault that occurs in copy_from_user() doesn't kill the process like it would if it is triggered by any other process-context code, or panic the kernel like it would if it occured in interrupt context - it simply resumes execution in a code path which returns -EFAULT to the caller.
regarding "how bout copy_to_user since the kernel is passing on the kernel space address,how can a user space process access it"
A user space process can attempt to access any address. However, if the address is not mapped in that process user space (i.e. in the page tables of that process) or if there is a problem with the access like a write attempt to a read-only location, then a page fault is generated. Note that at least on the x86, every process has all the kernel space mapped in the lowest 1 gigabyte of that process's virtual address space, while the 3 upper gigabytes of the 4GB total address space (I'm using here the 32-bit classic case) are used for the process text (i.e. code) and data. A copy to or from user space is executed by the kernel code that is executing on behalf of the process and actually it's the memory mapping (i.e. page tables) of that process that are in-use during the copy. This takes place while execution is in kernel mode - i.e. privileged/supervisor mode in x86 language. Assuming the user-space code has passed a legitimate target location (i.e. an address properly mapped in that process address space) to have data copied to, copy_to_user, run from kernel context would be able to normally write to that address/region w/out problems and after the control returns to the user, user space also can read from this location setup by the process itself to start with. More interesting details can be found in chapters 9 and 10 of Understanding the Linux Kernel, 3rd Edition, By Daniel P. Bovet, Marco Cesati. In particular, access_ok() is a necessary but not sufficient validity check. The user can still pass addresses not belong to the process address space. In this case, a Page Fault exception will occur while the kernel code is executing the copy. The most interesting part is how the kernel page fault handler determines that the page fault in such case is not due to a bug in the kernel code but rather a bad address from the user (especially if the kernel code in question is from a kernel module loaded).