Like how do I describe if someone is doing symbols with their hands like this? I want to describe specific hand formation but that seems like it’ll be a whole paragraph just for one second of saying that his hands are doing a symbol.
I feel like your question is a bit too specific, so my answer is going to be a little more generic.
When describing something with very fine detail it's easy to provide too much information and lose the reader, because we often think too visually and not enough about story.
He brought his hands together, fingers flat at first, then lowered all but his middle and little fingers, bent slightly at the knuckles, pointing upwards, forming a symbol. Then the next symbol, he rose his index, dropped his little finger and put his palms together. The next...
Reads quite badly, because we don't really care how his hands are shaped exactly, but as a reader, we care about the results.
When we read, we interpret things through our own lenses. When we watch anime, we see the pictures as they're drawn. It's a good idea to embrace the fuzziness of writing, not to try and paint with your words as precisely as a picture on a screen.
He brought his hands together, his fingers pointed out like a beak, forming the ninja sign for bird. Then, the symbol for ram - palms together, index and middle fingers pointed high, focusing on that point, focusing his chakra there until his fingers burned and his breath caught in his throat...
In this second one I barely bothered describing the symbols. Some readers will imagine the bird sign very differently to others. Think about why your character is doing these things and what the result is. If someone wants to imagine the thumbs spread like wings for the bird, let them. What damage does that do to your story?
If you must define it in a way that fans can say is right or wrong, add it in an appendix at the back, where diagrams are wanted and expected. Bogging down your prose with those details will not only upset the flow, readers will not imagine it precisely the way you want them to no matter how much you describe it.
I don't know what "Naruto-like hand symbols" are, but from the context of the question, I am going to assume they are some kind of complex hand gestures used to cast spells (or something similar). So let us proceed from there.
Firs thing you need to ask yourself is: do you need to describe each particular gesture combination? Do the specific movements further your plot? You could, for instance, establish that spells are cast by means of complex hand waving, and proceed from there. This need not be boring: each set could be "like a dance", or "like a karate master going through a series of katas", etc. The important thing is, instead of talking of specific "spells", you establish the whole form.
Having established the form, you want more specifics? You can give the symbols names. Like katas or asanas or pas have names. Again, having established the form, the reader doesn't need to know specifically which hand goes where at what time - give a general image, and the reader will fill in the blanks.
You want to establish that some symbols are complicated, require precision, etc.? You can talk about training. You can mention an incorrectly positioned finger causing the spell to go wrong (or do nothing at all). You can mention a character being "unable to bend his arm into that angle", or hurting themselves through bad technique, or just being physically tired afterwards. Again, let the reader fill in the blanks, create their own image in their minds.
Seeing a well-executed sequence of movements on screen is awesome - it's like a dance, it has aesthetics, it has impact. Reading about a series of movements is boring: it's a dry list of hands going from one position to another. It takes far longer to read about a movement than to do it, so everything feels in "slow motion". And worst of all, most readers are not proficient in dance or martial arts, so it would be far too easy for them to lose track of what's going on. When a reader loses track of what's going on, they become bored. And that's the one thing you want to avoid at all costs.
Just spent some time reading up on Naruto. It seems that they are gestures that Ninjas can use to summon certain types of energy in combat. I think therefore the signs should not really be the focus of any description.
Additionally, I think that practically, a skilled Ninja would be using them so rapidly that they would be a meaningless blur to the casual bystander (aka reader).
Instead focus on describing the effects of the Naruto-like gestures. This could be in terms of a description of the energy flow, the effect it has on the intended target or, better, both.
Once you break it out like that, a description of fingers and hands is replaced by one of energy and effect, which becomes much like describing any interaction between two bodies.
I am going to expand on a part of Galastel's answer.
Robert Jordan managed to abstract a whole fighting style by stamina stances and moves words. He would write something like "He shifted from Parting the Wave to Charging Bull.." We do not know what those things mean exactly, but we can get aa mental image.
With hand gestures this is a hundred times easier. Considering that in Naruto they are pretty much spell casting and not fighting the movements just have some meaning. You can simply write "He made the symbols: serpent, rain, death with his fingers, as fire erupted all around" The reader will get the mental image that you are looking for.