I wondered how memory access is handled \"in general\" if ,for example, 2 cores of CPU try to access memory at the same time (over the memory controller)? Actually the same
The short answer is "it's complex, but access can certainly potentially occur in parallel in certain situations".
I think your question is a bit too black and white: you may be looking for an answer like "yes, multiple devices can access memory at the same time" or "no they can't", but the reality is that first you'd need to describe some specific hardware configuration, including some of the low-level implementation details and optimization features to get an exact answer. Finally you'd need to define exactly what you mean by "the same time".
In general, a good first-order approximation is that hardware will make it appear that all hardware can access memory approximately simultaneously, possibly with an increase in latency and a decrease in bandwidth due to contention. At the very fine-grained timing level access one device may indeed postpone access by another device, or it may not, depending on many factors. It is extremely unlikely you would need this information to implement software correctly, and quite unlikely you need to know the details even to maximize performance.
That said, if you really need to know the details, read on and I can give some general observations on some kind of idealized latpop/desktop/server scale hardware.
As Matthias mentioned, you first have to consider caching. Caching means that any read or write operation subject to caching (which includes nearly all CPU requests and many other types of requests as well) may not touch memory at all, so in that sense many cores can "access" memory (at least the cache image of it) simultaneous.
If you then consider requests that miss in all cache levels, you need to know about the configuration of the memory subsystem. In general a RAM chips can only do "one thing" at a time (i.e., commands1 such a read and write apply to the entire module) and that usually extends to DRAM modules comprised of several chips and also to a series of DRAMs connected via a bus to a single memory controller.
So you can say that electrically speaking, the combination of one memory controller and its attached RAM is likely to be doing only on thing at once. Now that thing is usually something like reading bytes out of a physically contiguous span of bytes, but that operation could actually help handle several requests from different devices at once: even though each devices sends separate requests to the controller, good implementations will coalesce requests to the same or nearby2 area of memory.
Furthermore, even the CPU may have such abilities: when a new request occurs it can/must notice that an existing request is in progress for an overlapping region and tie the new request to an old one.
Still, you can say that for a single memory controller you'll usually be serving the request of one device at a time, absent unusual opportunities to combine requests. Now the requests themselves are typically on the order of nanoseconds, so many separate requests can be served in a small unit of time, so this "exclusiveness" fine-grained and not generally noticeable3.
Now above I was careful to limit the discussion to a single memory-controller - when you have multiple memory controllers4 you can definitely have multiple devices accessing memory simultaneously even at the RAM level. Here each controller is essentially independent, so if the requests from two devices map to different controllers (different NUMA regions) they can proceed in parallel.
That's the long answer.
1 In fact, the command stream is lower level and more complex than things like "read" or "write" and involves concepts such as opening a memory page, streaming bytes from it, etc. What every programmer should know about memory serves as an excellent intro to the topic.
2 For example, imagine two requests for adjacent bytes in memory: it is possible the controller can combine them into a single request if they fit within the bus width.
3 Of course if you are competing for memory across several devices, the overall impact may be very noticeable: a reduction in per-device bandwidth and an increase in latency, but what I mean is that the sharing is fine-grained enough that you can't generally tell the difference between finely-sliced exclusive access and some hypothetical device which makes simultaneous progress on each request in each period.
4 The most common configuration on modern hardware is one memory controller per socket, so on a 2P system you'd usually have two controllers, also other rations (both higher and lower) are certainly possible.
There are dozens of things that come into play. E.g. on the lowest level there are bus arbitration mechanisms which allow that multiple participants can access a shared address and data bus.
On a higher level there are also things like CPU caches that need to be considered: If a CPU reads from memory it might only read from it's local cache, which might not reflect that state that exists in another CPU cores local cache. To synchronize memory between cache instances in multicore systems there exist cache coherence protocols which are are implemented in the CPUs. These have to guarantee that if one CPU writes to shared memory the caches of all other CPUs (which might also contain a copy of the memory locations content) get updated.