Let's start with the basics.
Locate a set of jumper cables and confirm they're in good condition.
Locate the batteries on both the dead vehicle and the running vehicle (they're usually under the hood, but may be in the trunk or elsewhere -- check your owner's manual).
Park the operable vehicle next to the dead vehicle, close enough that the jumper cables can stretch between both vehicles' batteries. Ensure the ignitions on both vehicles are off.
Attach one of the jumper cable's positive (red) clamps to the dead battery's positive terminal (marked with a "+" -- it's often covered with a red cap).
Attach the other positive clamp to the good battery's positive terminal.
Attach the negative (black) clamp to the good battery's negative terminal.
Returning to the inoperable car, attach the black clamp on that end to a piece of unpainted metal under the hood at least 1 foot away from the dead battery. (See "Keep yourself safe," below.)
Start the engine of the operable vehicle, running it to 1,500 rpm for at least a few minutes.
After several minutes, the dead battery should have enough charge to start the inoperable car.
Attempt to start the inoperable vehicle. It should at least turn over. If it fails to start after a few cranks, return to Step 8. If the vehicle starts, continue to Step 11.
Remove cables in the reverse order that they were applied.
Drive the vehicle with the previously dead battery for about half an hour to recharge it before turning the engine off.
Need more info? Here's how to jump-start your car in depth
So you've cranked your ignition, and instead of your car firing up and raring to take you to your next destination, all it does is make a rapid clicking sound, or perhaps no sound at all. Looks like you've got yourself a dead battery.
If you've got a set of jumper cables in your trunk and another (operable) vehicle nearby, you can be back on the road in less than 10 minutes -- even less if you carry one of those portable jump-starters with you.
Identifying conduction points
Typically your battery is under your hood, but sometimes it can be in the trunk, or even under the floor of the passenger compartment. If you open your hood and there's no battery to be found, consult your owner's manual.
Once you've located your car's or truck's battery, identify the positive and negative terminals. They're the metal posts protruding from the plastic casing and they'll have plus (+) or minus (-) symbols near them.
Some auto manufacturers go the extra mile and color-coordinate battery terminal connection points with red for the positive side and black for the negative side. Once you've identified your battery's positive and negative terminals, do the same for the operable vehicle you're using to jump-start your car. Once you've done that, it's time to start making connections.
Keep yourself safe
With the operable vehicle switched off, begin the connection process by attaching a red cable clamp to your dead car's positive terminal. As long as any part of your jumper cables are connected to a power source, ensure the cable clamps never touch one another. This could provoke sparking that could increase the risk of a fire.
Walk over to the operable vehicle and connect the other red clamp to that battery's positive terminal. While you're there, go ahead and attach the black clamp to the negative terminal. Walk back over to the inoperable vehicle and complete the circuit by attaching that side's black clamp to a piece of unpainted metal under the hood that's ideally more than a foot away from the dead battery.
Do not complete the circuit by attaching the black clamp to the dead battery's negative terminal. Doing so is a recipe for an explosion.
Start your engines
Once you've made all four connections at the three terminals and single ground point, start the engine of the operable vehicle and gently depress the accelerator to raise the engine's speed to about 1,500 rpm. This allows the alternator of the running vehicle to support the charging process.
After the running vehicle has charged the other car's dead battery for a few minutes, try starting the vehicle with the dead battery. If your dead car fires up again, you may want to yell, "It's alive!" With those theatrics out of the way, you can now begin disconnecting the terminals in the opposite order that you connected them.
If you had to borrow jumper cables from a stranger, thank them profusely and let them know you're headed to the auto parts store to pick up your own set, because jumper cables are an absolute essential to have in your car at all times. If that auto parts store is a few towns over, even better -- an extended drive can give your car's alternator sufficient time to charge a battery that just had a near-death experience.