You can go two ways with this, depending on how "leaky" you want the mystical elements to be. Is it sunshine, pink bunnies, and technicolour in the Fairy Woods even before you meet a fairy, or is the world mundane with the fantastical elements playing more of a "This can't be real, I don't believe my eyes" kind of role in decisively mundane surroundings?
Fantastic things in mundane places
Simply put, don't try to transition. State the facts of the fantastic elements as your PCs perceive them, and nothing more.
State the fantastic as it happens. The way the facts violate the expectations of the rest of the established setting will do your work for you. Describe it in the same terms, themes, and "colour" that you do ordinary life in the setting, which will ground it in reality. Its unreal elements, narrated matter-of-factly, will actually sound more fantastical for the contrast.
The sweat and grime of the trail is getting to you around noon, when you stop to drink at a stream off the road. Refreshed, you notice a dark cave mouth on the far bank. Noxious fumes drift from it, and you become aware of an uncanny stillness which no birdsong disturbs. Then, an unearthly rumbling sigh issues from the crack in the earth.
(the PCs investigate and disturb something)
An enormous, stinking lizard drags itself from the depths. Smoke billows from its nostrils and its eyes are orbs of flame where a beast should have whites and pupils. It pulls the rest of its carcass free of the cave, revealing tattered wings like those of a bat and a wickedly barbed tail …
Describing the fantastic in mundane terms maintains the possibility of plausible deniability, and plausible deniability of the fantastic can keep your players grounded in the mundane. "Was that a dragon we fought? Well, we'll definitely brag that it was a dragon, but maybe that was just a really big lizard… It was a weird foreign country like [country only two borders away] after all, who knows what kind of barbaric beasts they normally have…"
Of the two options this is really my preference for maintaining my own grounding in the mundane. It just seems to work better, possibly because it forces me to recontextualise the fantastic occurrences in mundane terms, keeping my own "camera perspective" firmly on the mundane side of reality.
Fantastic lands border the mundane ones
If you want a world (or parts of the world) to have entire regions that are not mundane, you need some tricks to indicate when the characters are transitioning between their familiar, reliable world to the lands that are "not in Kansas anymore". Much like a movie/TV character's musical theme can subtly telegraph when they're having a spotlight scene, you want some tools that signal that the surroundings are changing.
You can do this by straight-up telling them, when the altered nature of the places is perceptible. Just extend the matter-of-fact statements about weirdness to the environment. Where there are (e.g.) uncanny, eerie places that the characters would "sense", just say so:
This place is eerie and uncanny. It feels wrong in your bones.
or for (e.g.) a nice-fantastical locale:
There is a lightness to the air that seeps into your skin, and everything feels brighter.
You want your players to know that the place is unusual, so tell them (via addressing their characters) that it is so, in plain language.
For a more subtle signal, you can use certain kinds of language to distinguish the mundane realms and the fantastic realms. A fairy wood might be "fresh", "bright", and devoid of the language that describes the grime of the mundane realms. You can narrate more slowly, in a more relaxed manner, giving it a bit of a dreamlike quality.
You can use different metaphors. A fantastic realm might get narrative descriptions that frame everything in terms of clean edges and elements in motion:
The flaming leaves of the autumn forest burn bright as the sun sets behind the knife edge of the mountains. The stars come out like hard diamonds, and the bright silver of the moon pours over the forest.
A different fantastic realm might get metaphors about swords, blood, and smoke. Another might be bones and death. Whatever metaphors you like, you can divide them up and say "these are for the mundane places, and these are for the fantastic places", and players will pick up on the distinct feel of different places, even if they can't put their finger on why.