Capturing is where you wait for your dog to do a behavior you like and reinforce that behavior to increase that chances that the dog will choose that behavior more frequently in the future. Every time your dog does a behavior that you want to be repeated, you simply reinforce it appropriately with food, petting or praise. Once your dog is repeating the behavior a few times a day, you can start to add in the cue word you want for the behavior. Then once the dog understands the cue you can lure them into position. And finally you can start to proof that behavior by calling for it in various environments.
For example: I want Azul to calmly lay by me during meal time. So when he was very young, I rewarded him with kibble for laying calmly while I ate. We did this in a variety of places; near the kitchen table, near me on the couch, in the car, etc. Slowly I phased out the kibble and switched to a larger reward at the end of my meal.
I also did the same thing when we were visiting with friends. Azul could get up and play, sniff, whatever when he chose to. But if he chose to lay calmly at my side, he got rewarded with kibble and petting.
Science has proven that animals will continue to do behaviors that are reinforced. Capturing in training sessions is based on that principle. You basically ignore behaviors you don't like, such as putting their puppy paws on you and reward a calm sit by your feet. If you don't reinforce good behaviors, the things you don't want such as jumping on people often become self reinforcing because it doesn't take long to learn that jumping on people will get a response. It might be cute for a puppy but if you don't want a full grown adult dog to do a behavior, don't reinforce it. It's much easier to do this with young puppies but even older adults can learn by capturing the good behaviors you want and ignoring or preventing the behaviors you don't want repeated.
Luring is commonly the first type of training we do with young puppies and most of us do it whether we realize it or not. So I'm going to talk about this from the puppy perspective. But it's also important that luring doesn't become your only training method or you really limit yourself and your dog's ability to learn.
Keep in mind that puppies need to be puppies, so keep expectations realistic for your pup's age & breed. Second, there is more to training a pup than teaching them cues/commands to obey. And finally all dogs are different so move at your pup's pace.
The very first thing to teach a puppy often comes up. For me, that's relationship building. I start with teaching pup that good treats (even kibble) comes from my hands. I start this on day one, sometimes before we even make it home. I don't use any words, but maybe some fun playful noises and/or puppies name. Each time the pup looks at you, present your hand very close to the pup's nose. Eventually you can hold your hand further away and pup will look for your hand when making that sound or say their name. That's step 1 in creating a strong bond. And that leads to step 2 and warming up your pup's brain for future learning using the luring technique.
Step 2 is using luring to get behaviors that you eventually want to put on cue. Holding a treat slightly above the puppies head and slowly moving it toward pup's back can be a great way to lure the pup into a sitting position. Trainers often use the phrase, "Don't name it, till you love it!" Or in other words don't start adding the cue until you can successfully lure your pup into the position you want. I use this training method to teach young pups several positions. And this brings us to #3.
Step # 3 is choosing the order in which you train specific behaviors and you can use luring to your advantage if you focus on behaviors your puppy enjoys doing naturally. There is no hard and fast correct way to train your pup. No two pups are exactly the same. Nothing says teach sit the first week, down the second, etc. Watch your pup and how well you can communicate with each other. If a pup offers a down before a sit, work on that first. This also means don't compare your pup to your neighbor's or other people online. You are different, your pup is different, so don't force yourself to stick to someone else's timeline. Enjoy your puppy & let your puppy be a puppy with lots of playtime, bonding, and finding out what works for you.
And this doesn't mean that you can only use luring to train early basic behaviors! As you grow as a team, you learn how to encourage your dog to make good choices and often you will use luring to provide that encouragement. Teaching a dog to touch a hand target can help you expand your luring technique without using a food lure all the time.
Another term commonly used when discussing capturing is "back chaining." Back chaining behaviors can be used with different training methods, but it's simplest to start during capturing training. If you want to teach your dog to go potty on cue, you often start giving your cue while your puppy is going potty then as time progresses you back up your cue earlier and earlier until you can give the cue and your puppy will almost immediately go potty.
Another form of back chaining involves linking behaviors together by teaching the last behavior first and working backwards until the whole chain has been taught. A great example of this is the hand delivered retrieve that is commonly taught in 4 stages; pick up the object, hold it in your mouth, bring it to me, and drop the object in my hand. It doesn't really matter which order you teach each of those behaviors independently, but when creating the behavior chain you really want to start with the last one first which is often the hardest, drop.
Now this might should challenging because how can you teach drop if your dog doesn't put things in their mouth. That's a very valid point! If your dog was trained to not chew on people things at an early age, they may really struggle with even picking up any item in the first place. That's a case of where you may not want to use back chaining. Another example of when NOT to use back chaining is when the end behavior is more complex the the starting behavior. I have trick called "take a nap" which is a basic twist on play dead but it requires the dog to first lay down, then either place their head down on the floor or lay on their side in a relaxed position and hold still until they are released to wake up. I can't very well teach my dog to lay with his head down until I my dog already knows how to lay down on cue. And I can't very well teach my dog to hold still in this position until I can get them more comfortable in this position.
So when would I use back chaining for teaching a complex behavior? The simple answer is any time I want to expand on what my dog already knows to bump it up to the next level. Think back to the puppy stage, at first you watched them like a hawk and rushed them out the door to go potty at an slight signal they may need to go. But eventually you want to be able to teach them to give you some kind of a signal that they need to go so you don't have to watch them like a hawk. Then as they get older, you may need a different signal that can be given in different environments when your not at home, especially if you travel with your dog like I do. You can also use back chaining to increase distance or time to a behavior that is already known. For example, I teach my dogs to find the car, first at home in my driveway then in parking lots. Once they can find the car, I start going from the checkout lane to the car until they are successful in that. Then I add the step of finding the checkout lane from various locations in the store. Then if I need to make an hasty exit, I can tell me dog to find the car from nearly anywhere in the store and they will take me past the checkouts to the car. I can then use this teach other common places that I may need to go regularly like finding a bathroom or a chair to sit in. I know this steps more into the Service Dog world with advanced training, but the method of back chaining is used in teaching many dog sports and competitions too. Learning to use back chaining effectively will really up your training abilities.
Here is a short video of how I taught Azul to settle at my feet, under my chair or under a table while I eat my meals. This video demonstrates luring Azul as a young puppy with food. But since I also captured this behavior regularly once the behavior was learned it because second nature and now is an automatic behavior that just happens without the need for reinforcement all the time. He does still get reinforced for doing it regularly, he just doesn't need it all the time!