Hands! Possibly the most difficult parts of the human body to figure out where to put them. Nothing feels more awkward than not knowing where they should go. But when it comes to trying to bond with your pigeon, good news: you are going to learn where to put your hands right now! There are definitely things you should and shouldn't do with them, and this section will go over as many of these as possible.
An important thing to keep in mind right at the start is that our hands are not shaped especially conveniently for bonding with pigeons. Pigeons do much of their bonding behaviors with their heads and necks, sometimes incorporating their wings and other bits of body posture. Our hands don't particularly look like bird heads—at least not how we typically hold them! They do, however, look somewhat like bird feet. And, if you stretch your imagination, a little bit like bird of prey feet. Whether or not pigeons make this connection, one thing is fairly obvious: most pigeons do not like being directly reached for.
As a general trend, reaching for a pigeon palm-down from above usually causes a stronger reaction (and not a good one). A hand that is palm-up and lower than the bird is generally less alarming. However, when you want to provide an opportunity to interact with your hand, the back of your hand is usually not as frightening. It may be because your pigeon recognizes you aren't in a good position to grab it, it may be that the "bird talon" shape facing away is less inherently scary, or it could be something else entirely—but introducing a hand-shy pigeon to hands often goes better by letting them get used to the back-side before the palm-side.
As mentioned above, pigeons generally are not very comfortable being reached at directly.
There is a big reason why thinking about this consciously is useful: as a human being, you've probably been taught to hand objects (whether a pencil, a snack, or anything reasonably small you are giving to someone else) directly to the person you intend to give the item! Pigeons generally don’t like this! So what is a better method to offer a pigeon you're trying to bond with a snack?
There are several options for you:
This discomfort about reaching directly at them will often fade over time. As your bird gets more comfortable, sometimes pausing with your offering a few feet away where your bird can see it, and allowing them a chance to see you are approaching with something and allow them to become interested is all that is needed to make them comfortable.
Just remember: they are prey animals! They have good reason to be startled to realize your hand is on a direct trajectory to them with no warning!
It is possible to create a cue for your pigeon to welcome them to your space. A pigeon already bonded to you can likely easily pick this up through the positive reinforcement of your attention—a food motivated pigeon can pick up the same thing.
What cue you develop is up to you! However, it may be more effective to include a physical movement if your first thought is to have an audio cue. A quick one-two tap on a new pile of treats (along with whatever short word you might add) can quickly create an association that when you tap, there is something good to be found. This can then be transferred to draw attention to good perches (perhaps next to you) or items of interest like toys, or to invite your bird to a bed for pets.
As prey animals, learning that you are trustworthy and will not harm them is important to a pigeon's sense of safety. Here are some things that can contribute to that feeling.