The Fire-Making Charm
Incantation: Incendio (‘in-SEN-dee-oh’)
Wand Movement: Curved flick up and down (as a flame)
Focus: The target to be ignited
Willpower: Low to very high, depending on the distance of the target and the difficulty of igniting the target.
Concentration: None for a simple ignition; moderate concentration on the target should be maintained for a continuous stream.

The Fire-Making charm is one of the oldest-known spells, its incantation and wand movement both simple and elegant. The incantation is a direct word found in the ancient Latin language, a precursor to many modern-day languages including English, Spanish, French and Italian, to name a few. Few spells demonstrate such direct ties to their origin language, and fewer have a wand movement so symbolic of its effects.

One challenge to casting the Fire-Making charm is that it requires a fair bit of willpower and experience in addition to just the wand movement and the words. Other elementary charms, such as the Levitation Charm, produce the same effect for a first-year as it does for an accomplished wizard; the only real difference is how much they can levitate. The Fire-Making charm, on the other hand, grows in finesse and power as the user does. Anything from a faint puff of smoke to a controlled ignition at distance are possible.

The first-year student should be able to light a candle with this spell from several inches away. Early attempts might produce a bit of smoke or heat, and for this reason it's best to practice in an open area away from flammable materials. 

With more experience and practice, the user can typically make a small stream of fire flow from the tip of their wand, like a flamethrower. The distance this stream can travel is usually dependent upon just how much willpower is applied. This usage of the charm causes the air itself to be set alight in the direction specified though it still isn't very elegant.

A fully-experienced witch or wizard is able to target a distant object or location for the ignition and avoid excessive use of magic to achieve their goals. It's still difficult to target someone or something on the move, and as the counter for this charm is easy and takes but a moment, it has fallen out of favor in combat in recent memory.

The Locomotion Charm
Incantation: Locomotor (‘LOH-koh-moh-tor’)
Wand Movement: Full circle with an upward flick toward the target at the end, then pointed where the object should go.
Focus: The target object
Willpower: Moderate to very high, depending on the distance and weight of the object.
Concentration: Minimal concentration should be maintained on the object.

The Locomotion Charm, not to be confused with other charms typically classified as "Flight" Charms, is functionally similar but theoretically very different from other similar charms. The charm creates a thin barrier only a few inches (several centimeters) between whatever is targeted and the ground. The main purpose of the charm is to move its target from one location to another.

The Locomotion Charm has very interesting linguistic roots. It is the combination of two word from ancient Latin. "Loco" means place or location, while "motor" means to move. Taken together it means "move to a place", which is exactly what the charm does.

It is usually useful to specify the target of the spell verbally as well. If you want to target a nearby trunk, as most students do when moving theirs around, you can say Locomotor Trunk to make the target clearer. Some students find the spell not working for them when it was simply that they did not focus enough on their target and ended up moving dust or something else around that they had not intended.

The Locomotion Charm is also useful because it can remain active with very little concentration. The caster must spend a small bit of effort keeping the charm going, but otherwise they could cast another spell without having to recast the Locomotion Charm afterward. After the target is chosen, the caster simply points toward the direction where the object should go. Of course, in the beginning the object may swerve and shudder as it moves. With a bit of practice and finesse, it usually becomes a rather trivial matter, much like moving a shopping trolley around a store.