Multithreading vs multiprocessing
To answer the first question: The best approach is to just use multithreading techniques in your code until you get to the point where even that doesn't give you enough benefit. Assume the OS will handle delegation to multiple processors if they're available.
If you actually are working on a problem where multithreading isn't enough, even with multiple processors (or if you're running on an OS that isn't using its multiple processors), then you can worry about discovering how to get more power. Which might mean spawning processes across a network to other machines.
I haven't used TBB, but I have used IPP and found it to be efficient and well-designed. Boost is portable.
Multithreading means exactly that, running multiple threads. This can be done on a uni-processor system, or on a multi-processor system.
On a single-processor system, when running multiple threads, the actual observation of the computer doing multiple things at the same time (i.e., multi-tasking) is an illusion, because what's really happening under the hood is that there is a software scheduler performing time-slicing on the single CPU. So only a single task is happening at any given time, but the scheduler is switching between tasks fast enough so that you never notice that there are multiple processes, threads, etc., contending for the same CPU resource.
On a multi-processor system, the need for time-slicing is reduced. The time-slicing effect is still there, because a modern OS could have hundred's of threads contending for two or more processors, and there is typically never a 1-to-1 relationship in the number of threads to the number of processing cores available. So at some point, a thread will have to stop and another thread starts on a CPU that the two threads are sharing. This is again handled by the OS's scheduler. That being said, with a multiprocessors system, you can have two things happening at the same time, unlike with the uni-processor system.
In the end, the two paradigms are really somewhat orthogonal in the sense that you will need multithreading whenever you want to have two or more tasks running asynchronously, but because of time-slicing, you do not necessarily need a multi-processor system to accomplish that. If you are trying to run multiple threads, and are doing a task that is highly parallel (i.e., trying to solve an integral), then yes, the more cores you can throw at a problem, the better. You won't necessarily need a 1-to-1 relationship between threads and processing cores, but at the same time, you don't want to spin off so many threads that you end up with tons of idle threads because they must wait to be scheduled on one of the available CPU cores. On the other hand, if your parallel tasks requires some sequential component, i.e., a thread will be waiting for the result from another thread before it can continue, then you may be able to run more threads with some type of barrier or synchronization method so that the threads that need to be idle are not spinning away using CPU time, and only the threads that need to run are contending for CPU resources.
There are a few important points that I believe should be added to the excellent answer by @Jason.
First, multithreading is not always an illusion even on a single processor - there are operations that do not involve the processor. These are mainly I/O - disk, network, terminal etc. The basic form for such operation is blocking or synchronous, i.e. your program waits until the operation is completed and then proceeds. While waiting, the CPU is switched to another process/thread.
if you have anything you can do during that time (e.g. background computation while waiting for user input, serving another request etc.) you have basically two options:
use asynchronous I/O: you call a non-blocking I/O providing it with a callback function, telling it "call this function when you are done". The call returns immediately and the I/O operation continues in the background. You go on with the other stuff.
use multithreading: you have a dedicated thread for each kind of task. While one waits for the blocking I/O call, the other goes on.
Both approaches are difficult programming paradigms, each has its pros and cons.
- with async I/O the logic of the program's logic is less obvious and is difficult to follow and debug. However you avoid thread-safety issues.
- with threads, the challange is to write thread-safe programs. Thread safety faults are nasty bugs that are quite difficult to reproduce. Over-use of locking can actually lead to degrading instead of improving the performance.
(coming to the multi-processing)
Multithreading made popular on Windows because manipulating processes is quite heavy on Windows (creating a process, context-switching etc.) as opposed to threads which are much more lightweight (at least this was the case when I worked on Win2K).
On Linux/Unix, processes are much more lightweight. Also (AFAIK) threads on Linux are implemented actually as a kind of processes internally, so there is no gain in context-switching of threads vs. processes. However, you need to use some form of IPC (inter-process communications), as shared memory, pipes, message queue etc.
On a more lite note, look at the SQLite FAQ, which declares "Threads are evil"! :)