CPUs don't poll for interrupts, at least not in a software sense. With respect to software, interrupts are asynchronous events.
What happens is that hardware within the CPU recognizes the interrupt request, which is an electrical input on an interrupt line, and in response, sets aside the normal execution of events to respond to the interrupt. In most modern CPUs, what happens next is determined by a hardware handshake particular to the type of CPU, but most of them receive a number of some kind from the interrupting device. That number can be 8 bits or 32 or whatever, depending on the design of the CPU. The CPU then uses this interrupt number to index into the interrupt vector table, to find an address to begin execution of the interrupt service routine. Once that address is determined, (and the current execution context is safely saved to the stack) the CPU begins executing the ISR.
When two devices share an interrupt request line, they can cause different ISRs to run by returning a different interrupt number during that handshaking process. If you have enough vector numbers available, each interrupting device can use its own interrupt vector.
But two devices can even share an interrupt request line and an interrupt vector, provided that the shared ISR is clever enough to go back to all the possible sources of the given interrupt, and check status registers to see which device requested service.
A little more detail
Suppose you have a system composed of a CPU, and interrupt controller, and an interrupting device. In the old days, these would have been separate physical devices but now all three might even reside in the same chip, but all the signals are still there inside the ceramic case. I'm going to use a powerPC (PPC) CPU with an integrated interrupt controller, connected to a device on a PCI bus, as an example that should serve nicely.
Let's say the device is a serial port that's transmitting some data. A typical serial port driver will load bunch of data into the device's FIFO, and the CPU can do regular work while the device does its thing. Typically these devices can be configured to generate an interrupt request when the device is running low on data to transmit, so that the device driver can come back and feed more into it.
The hardware logic in the device will expect a PCI bus interrupt acknowledge, at which point, a couple of things can happen. Some devices use 'autovectoring', which means that they rely on the interrupt controller to see to it that the correct service routine gets selected. Others will have a register, which the device driver will pre-program, that contains an interrupt vector that the device will place on the data bus in response to the interrupt acknowledge, for the interrupt controller to pick up.
A PCI bus has only four interrupt request lines, so our serial device will have to assert one of those. (It doesn't matter which at the moment, it's usually somewhat slot dependent..) Next in line is the interrupt controller (e.g. PIC/APIC), that will decide whether to acknowledge the interrupt based on mask bits that have been set in its own registers. Assuming it acknowledges the interrupt, it either then obtains the vector from the interrupting device (via the data bus lines), or may if so programmed use a 'canned' value provided by the APIC's own device driver. So far, the CPU has been blissfully unaware of all these goings-on, but that's about to change.
Now it's time for the interrupt controller to get the attention of the CPU core. The CPU will have its own interrupt mask bit(s) that may cause it to just ignore the request from the PIC. Assuming that the CPU is ready to take interrupts, it's now time for the real action to start. The current instruction usually has to be retired before the ISR can begin, so with pipelined processors this is a little complicated, but suffice it to say that at some point in the instruction stream, the processor context is saved off to the stack and the hardware-determined ISR takes over.
Some CPU cores have multiple request lines, and can start the process of narrowing down which ISR runs via hardware logic that jumps the CPU instruction pointer to one of a handful of top level handlers. The old 68K, and possibly others did it that way. The powerPC (and I believe, the x86) have a single interrupt request input. The x86 itself behaves a bit like a PIC, and can obtain a vector from the external PIC(s), but the powerPC just jumps to a fixed address, 0x00000500.
In the PPC, the code at 0x0500 is probably just going to immediately jump out to somewhere in memory where there's room enough for some serious decision making code, but it's still the interrupt service routine. That routine will first go to the PIC and obtain the vector, and also ask the PIC to stop asserting the interrupt request into the CPU core. Once the vector is known, the top level ISR can case out to a more specific handler that will service all the devices known to be using that vector. The vector specific handler then walks down the list of devices assigned to that vector, checking interrupt status bits in those devices, to see which ones need service.
When a device, like the hypothetical serial port, is found wanting service, the ISR for that device takes appropriate actions, for example, loading the next FIFO's worth of data out of an operating system buffer into the port's transmit FIFO. Some devices will automatically drop their interrupt request in response to being accessed, for example, writing a byte into the transmit FIFO might cause the serial port device to de-assert the request line. Other devices will require a special control register bit to be toggled, set, cleared, what-have-you, in order to drop the request. There are zillions of different I/O devices and no two of them ever seem to do it the same way, so it's hard to generalize, but that's usually the way of it.
Now, obviously there's more to say - what about interrupt priorities? what happens in a multi-core processor? What about nested interrupt controllers? But I've burned enough space on the server. Hope any of this helps.