Foil Basics

Navigation

Grip
Hand Position
Footwork
Extension/Lunge

Basic Concepts of the Phrase

Right of Way
The Attack
The Advance-Lunge
Parry/Riposte
Remise/Reprise/Redoublement
Preparation

Offense

Simple Attacks
Straight Thrust
Disengagement
Glide
Coupe
Secondary Simple Attacks
Beat
Beat-disengage
Change Beat
Graze
Expulsion
Using Pressure

Defense

Basic Defense
The Simple Parry
The Riposte
Ceding Parries
Complex Defense
Circular Parry
Counter Attacks
Arrest/Stop Thrust
Disengagement in Time
Inquartata
Passata Sota

When You Can't Score The First Time...

Feints
Feint Direct
Feint-disengage
Feint by Glide
Ripostes with Feints
Counter Disengagement
Feint in Time

Misc. Considerations

Moves
Balestra
Appel
Fleche
Probing Actions
Concepts
Tempo
Countertime

Resources/Further Reading

Grip - There are two widely used categories of grips, French and Pistol (ergonomic). You gain more control with a French grip, but gain greater range of motion with a pistol. In modern foil, the choice is pistol. Both grips should be held with the pad of the thumb and the side of the tip of the index finger. In the case of French, the remaining three fingers should be wrapped for support, in the case of pistol, there are dedicate notches for these fingers to rest on.

French grip (left) vs. pistol (center and right)

Guard Position - Feet start shoulder width apart, dominant foot pointing straight ahead. The non-dominant foot is perpendicular to the dominant, or slightly angled towards the opponent (NEVER angle this foot backwards). The fencinge arm is bent so a straight line forms from the tip of the foil to the elbow, and is aimed at the opponents chest. The elbow should be approximately a handspan away from the torso. As for the other arm, ask your instructor. I don't care where you put it (although, do not rest it on the back hip) but many maestros smarter than I care deeply.
The back and torso must be straight, and head turned toward the opponent. Knees are also bent so that the upper body is "sitting" on the hips. Weight distribution should be 60%/40%, in favor of the non-dominant leg.

Proper Guard Position

Footwork - The single most important element in all of fencing. You can win with good footwork, and lose with bad.

Advance - The basics of the advance are: pick your dominant foot up, carry it about one foot length forward, and set it down, heel first. The non-dominant foot follows, but lands ball first. Think of it more of a carry, and less as a push.

An advance.

Retreat - Simply reverse the advance. In both maneuvers, make sure to maintain probably weight distribution and balance, in addition to keeping a shoulder's width of distance between the feet. Your head should remain at the same height throughout all footwork.

A retreat.

Cross-over/cross step - From the en garde position, carry the non-dominant foot across the line of the dominant foot, setting it down a little less than shoulder width in front of the dominant foot. Carry the dominant foot forward to return to proper en garde. Reverse to go backwards.

Cross step forward and back.

Extension/Lunge - A proper extension elongates toward the target at constant speed, with the arm finishing at shoulder height, and the torso learning slightly. Soon after the extension starts, lift the dominant foot, propel it forward by pushing off and straightening the left leg. While this thrust is happening, extend the left arm backwards to maintain balance.
During the lunge, the dominant arm must not break its extending motion, and the dominant knee, upon landing, should be in line with the dominant ankle.
To recover, push off the dominant leg, bend the non-dominant knee, and replace the dominant foot in en garde. Do not throw all your balance on your non-dominant leg during this procedure.

An lunge being executed against an opponent.