The other answers have already pointed out that there are two kinds of magic that are easily accessible to humans, dark magic and magic from a Primal Stone. As indicated in those answers, dark magic seems to be something that anyone can learn: Claudia knows dark magic because her father taught it to her, not becauze she inherited it from him. Similarly, the Primal Stone appears to be even easier to use than dark magic, and there is nothing to suggest that any human could not make use of it. In fact, dark magic and Primal stone magic seem to operate on the same principles: take an external source of power and draw upon it. Dark magic is of course far more disturbing, since it requires drawing the magic from living creatures, killing them in the process, which gives it a corrupting effect.
The more interesting point is that as of the end of S4, it is strongly implied that anyone can learn to perform Primal magic without a stone, albeit that it is much easier for beings with an innate magical connection, unlike what the other answers imply. As we see end of the second season and the beginning of the third, Callum has achieved the insight necessary to use Sky magic without the use of a Primal Stone, as we particularly see throughout seasons 3 and 4 through his extensive use. In order to do this, he had to really understand the nature of Sky magic at an intuitive level. While perhaps anyone could reach this understanding, it would not necessarily be equally easy for anyone.
What is perhaps most interesting about this is that it is seemingly subtly implied that this actually makes Callum better at Sky magic in some respects than many Xadian elves who are born with it. Concretely, Callum is able to manifest wings, which is not something that all Sky mages can do, and he is fairly early in his training. A creature who is born with Sky magic need not ever truly understand it, meaning that they get their powers "for free," but will not reach the higher levels without some investment of effort. And since they do not need to invest any effort, many do not bother. Callum could only attain his powers through a deep understanding of the magic, giving him a bit of a leg up.
Furthermore, apparently the startouch elf Aaravos has access to all six Primal sources. Nominally, he should only have an innate link to Star magic, which suggests that at some point over his long life, he learned how to use the other five. However, this is uncertain, because the Star Arcanum and startouch elves in general seem to be very different from anyone else in Xadia: it may well be that a connection to all six elements is normal for their mages.