If you're looking for driving/walking rules, see right-of-way. In fencing, we never use those little dash things.
Right of Way is the most important thing one needs to learn in order to pick up fencing. Getting good at fencing requires a whole lot more, but without learning Right of Way you'll be clueless as to why your opponent got a given point instead of you, even though you hit them just as hard/well.

-By the way, ignore all of this if you've decided to fence epee. Not only does epee have virtually no rules, it also has no Right of Way.

So this is the basic idea: when fencing foil or sabre, you take turns. When someone claims Right of Way, it means they have the authority to attack.

  • I attack.
  • Then you attack.
  • Then I'm allowed to attack after that.

Attacking out of turn will only score you a point if your opponent misses.

Who decides who goes first?
You do - based upon your actions. There are many times throughout a fencing bout when no one has Right of Way. For example - neither of you are taking the initative (you're both either being lazy, or patient) or both of you are taking the initative (you're bothing charging - this is usually ruled a simultaneous action. In the end though, after skirting around one another for a bit of time, someone is going to come out with the attack - initating an offensive move when your opponent does not claims Right of Way. It's a simple idea, but it takes a while to train your mind to react in the proper fashion.

My opponent has Right of Way. What do I do?
Take it away from him/her. This is key to fencing foil or sabre. There are three main ways to get Right of Way back after losing it:

  • Defense: Here you have two options - parry and dodge. Either of these options works equally well in theory and depending upon your style and ability you'll hopefully be flexible enough to use both - deciding at the necessary moment which to rely on.
  • Counter Offense:There are a range of more or less successful actions that fall into this category. A counterattack is not usually a wise idea. If you just lost Right of Way through a miss or parry you can always Remise. A stop cut is available in sabre. If your opponent is still some distance away and hasn't fully committed him/herself yet, Point in Line is an option. But: Battement is the typical solution that one chooses. Again - these are either attacks against your opponent or against his/her blade while they have Right of Way - if they hit you, you will lose the point even if you hit them too.
  • Outmaneuver: More effective and frequent than you might imagine, given that you essentially fight in a straight line. Outmaneuvering in fencing usually involves alternating the pace and size of your steps to throw off your opponent's rhythm. A slight pause or hesitation or your opponent's part will usually signal a loss of Right of Way. One note: this is far more effective a choice when fencing foil than when fencing sabre.

Is this realistic?
Yes and no. The idea behind behind Right of Way is three fold:

  1. It takes into account the idea that only a committed and plotted attack would be successful enough to actually hurt someone. Let's look at two common instances when both fencers hit one another. For the sake of argument we'll assume both are fencing sabre.
    • Attack - Counterattack: The fencer with attack has charged across the strip at the other fencer who is standing more or less still. At the last moment, the one being charged flails out and hits the charger (who also strikes). The idea in this case being, the fencer with the attack was the one of the two who had the force and intentionality to be deadly.
    • Attack - Parry - Riposte - Remise In this case, fencer A attacks, is parried by fencer B, fencer B then initiates an attack (a riposte) (because it's his turn) and instead of defending that attack, fencer A chooses to strike at fencer B again. In order to visualize this sequence, it is important to realize that fencers are trained not to pull back from your opponent when parried - it is easier to defend when your weapon is already extended. So, the action would look like this - fencer A strikes at fencer B's belly. (Attack) Fencer B turns his bell guard to his left and moves his hand all of four inches to allow fencer A's blade to land harmlessly on his guard. (Parry) Fencer B then forgets about Fencer A's blade lying a scant few inches away from belly, extends his weapon, and smacks Fencer A in the face. (Attack) Fencer A carries on with his attack, even though parried, and hits Fencer B in the stomach. (Remise) Again, the idea is that only Fencer B scored a hit that would be damaging or fatal. Not because of location of hit, but rather because the force of fencer A's action was stopped by the fencer B's parry, and the Remise itself would not have been powerful enough to cause harm.
  2. Right of Way also takes into account the idea that someone who has trained to duel with weapons that potentially could cause death would desire to protect themselves from harm. If you look at both cases used as example above, you can easily see how they would be extrapolated as suicidal gestures when fencing in a real life situation.
  3. Etiquette. The roots of fencing are planted in a deeply ritualistic society that had rules for how one is to comport oneself in every situation - dueling is no different. And since we're playing their game, we play by their rules.