Almost everything you do will be in the cache at the moment when you use it, unless you are reading memory that has been configured as "uncacheable" - typically, that's frame buffer memory of your graphics card. The other way to "not hit the cache" is to use specific load and store instructions that are "non-temporal". Everything else is read into the L1 cache before it reaches the target registers inside the CPU itself.
For nearly all cases, CPU's do have a fairly good system of knowing what to keep and what to throw away in the cache, and the cache is nearly always "full" - not necessarily of useful stuff, if, for example you are working your way through an enormous array, it will just contain a lot of "old array" [this is where the "non-temporal" memory operations come in handy, as they allow you to read and/or write data that won't be stored in the cache, since next time you get back to the same point, it won't be in the cache ANYWAYS].
And yes, processors usually have special registers [that can be accessed in kernel drivers] that can inspect the contents of the cache. But they are quite tricky to use without at the same time losing the content of the cache(s). And they are definitely not useful as "how much of array A is in the cache" type checking. They are specifically for "Hmm, it looks like cache-line 1234 is broken, I'd better read the cached data to see if it's really the value it should be" when processors aren't working as they should.
As DanS says, there are performance counters that you can read from suitable software [need to be in the kernel to use those registers too, so you need some sort of "driver" software for that]. In Linux, there's "perf". And AMD has a similar set of performance counters that can be used to find out, for example "how many cache misses have we had over this period of time" or "how many cache hits in L" have we had, etc.