Handseals
According to what is currently canon, you need to use elemental chakra to use elemental jutsu. However, this is contradicted by Sasuke using Katon jutsu as a child, because he was never canonically trained to convert his chakra to fire elemental chakra. (There's also the fact that, according to both Kakashi and Yamato, elemental training takes a long time and a lot of hard work, and it's extremely doubtful that a seven year old Sasuke was capable of such a thing.)
In light of this, I have created a system that will hopefully not only explain this seeming contradiction, but will also help deepen and enrich the concept of jutsu.
Handseals:
Handseals serve an important function to chakra users, in that they allow the user to mold and shape their chakra in the correct way to utilize jutsu. Because each handseal can shape and mold chakra in a different way, stringing multiple handseals together can create increasingly complex effects.
While it is a general rule of thumb that more powerful jutsu require more handseals (because they involve complex effects), this is not always true. Some of the most infamous and legendary jutsu are actually relatively simple at heart, and require only one or two handseals, if any at all.
However, while handseals are extremely important, they are also, at their core, a crutch of sorts, because they mold and shape the user's chakra for them. Identical affects could be accomplished through training and chakra control, and high-level chakra users or individuals with a high degree of control can easily drop certain seals from their jutsu, because those seals are no longer needed; they can mold their chakra in that manner without seals.
To this end, chakra control is essential to powerful chakra users, because it allows them to use their abilities and techniques with greater speed. The less seals you require, the faster you can fight and cast jutsu.
The Twelve Primary Handseals:
The twelve primary handseals act as the core handseals for chakra users. Each of the twelve handseals represents a different animal of the Zodiac, along with a different celestial house and planet.
The purpose of handseals is to mold and shape chakra, and to that end, different combinations of handseals have different effects.
The Elemental Handseals:
Among the twelve standard seals for jutsu, each of which represents an animal of the Zodiac, there are five seals that are special, in that they convert your normal chakra into elemental chakra for you automatically when used.
They are:
Tora (Tiger): The Fire seal.
U (Rabbit/Hare): The Wind seal.
Tatsu (Dragon): The Water seal.
Mi (Snake/Serpent): The Earth seal.
Tori (Bird/Rooster): The Lightning seal.
These elemental handseals are used by ninjutsu users who have not yet mastered or trained in elemental manipulation. They are, just like the other seven "normal" seals, crutches, as they allow someone who normally has no power over a given element to make use of jutsu that use that element.
However, these five handseals are considered to be more vital and important than the other seven, because unlike those seven, the elemental seals cannot be dropped or ignored simply by improving one's control. Only mastery of an elemental training exercise would allow someone to drop an elemental handseal, because only mastering the ability to shift the elemental nature of their chakra to another element would render an elemental seal obsolete.
Beyond the Twelve Core Seals:
While the twelve primary handseals cover the basics for most chakra use, there are still some techniques that require a more exotic or extreme touch. These techniques and jutsu utilize what are known as "off-seals" and "secret seals", or seals that are not part of the twelve core seals known by all shinobi.
These seals serve two primary functions:
1.) To provide an effect or shape chakra in a manner that would be impossible with the twelve core seals (in this context, 'impossible' is defined as "far too many to be of any use", as there are actually very few effects that could not be created with the twelve core seals, provided they were used in the correct (often extremely long) sequence and given enough time. However, an effect that would otherwise take hundreds or thousands of seals to create is considered "impossible" for the sake of the term).
2.) To keep certain specific techniques and abilities exclusive to a group, organization, or family. Most powerful clans have created their own secret handseals, and the clan's hijutsu (secret techniques) are designed to require this handseal to operate properly. Most villages also possess one or more secret seals, which are usually tied into that villages secret or forbidden techniques, and are jealously guarded.
As one might imagine, secret seals are highly sought-after, and considered to be the foundation of a clan's or village's power, as they represent that group's capacity to do things that others cannot.
To this end, clan and village hijutsu are only taught to individuals who are also trained in control to drop that secret seal. This ensures that the secret to a village's or clan's power cannot be stolen or imitated; as long as the seal or seals required remains a secret, the hijutsu cannot be copied or imitated.
As to the function of hijutsu seals, they are nearly limitless in potential. Most are the result of generations of experimentation and practice, and are highly refined as a result. Most provide unusual or exotic effects to a jutsu, often far more extreme than anything a normal handseal could accomplish. There are rumors of hijutsu seals that can do everything from making illusions semi-solid, to allowing the user to acquire animalistic traits, to opening up whole new elemental routes (rumors of "Metal jutsu" have persisted for generations), and even to allowing the user to fuse elemental chakras without a bloodline or blood limit that allows them to do so (rumors also persist of a secret "Ice seal", with claims ranging from the royal family of Snow country to a handful of clans that reside within the Hidden Village of Mist).
Known hijutsu seals in canon include:
The cross-shaped seal required for Kage Bunshin.
The triangle-shaped seal required for Yamanaka hijutsu.
The Sharingan:
A specific Kekkei Genkai, namely the Sharingan, bears mentioning, because one of its powers is uniquely tied into the concept of handseals.
Namely, it's ability to "copy" (some would claim "steal") jutsu and techniques.
One of the Sharingan's most infamous abilities, the ability to snatch jutsu from someone else, is, in fact, an exercise in memory and visual deconstruction. At will, a Sharingan user can choose to memorize whatever they see with their Sharigan.*
In the case of jutsu, this means that they memories the sequence of handseals used to achieve the effect. Thus, an Uchiha isn't "copying" a jutsu so much as they are remembering the handseals needed to perform those jutsu.
This is a great boon to young and inexperienced Uchiha, who often find themselves in direct contest with others who make prodigious use of handseals. To older and more experienced Uchiha, however, the ability loses much of its application in the field of ninjutsu, because their opponents are both skilled enough to know how to drop multiple handseals from their jutsu and wise enough to know to drop as many seals as possible, lest they be on the receiving end of their own techniques.
It is also rumored that the ability to effortlessly memorize handseals has made many Uchiha lazy in regards to chakra control and refinement, as few Uchiha are ever seen fighting without making use out of most or even all of the seals needed to cast the jutsu. Said claims are rebuffed by the Uchiha, who say there's nothing to them.
Other rumors, like the Sharingan actually forcing the Uchiha to use all the handseals of jutsu they've copied as a direct side-effect of copying them in the first place, are similarly rebuffed.
* Or so the Uchiha claim. Other, non-Uchiha accounts claim that the Uchiha cannot control what they remember, and simply remember everything they see when their Sharingan is active, regardless of what it might be or how important (or trivial) it is. Whether or not this is true is unknown, though it could potentially explain the occasional mental degradation among Uchiha; if their Sharingans were preventing them from forgetting things, their mental capacity would slowly degrade, their minds robbed of the basic ability to "clean house" and forget unimportant information. Given enough time and overexposure, this would almost certainly drive an individual mad, though exactly how that madness would manifest would depend entirely on the individual (i.e. obsessions, obsessive-compulsive, fits of insanity, uncontrollable physical or verbal tics, ect).