Dipoles have the 2 wires going to each leg of the antenna completing the circuit.
Big AM towers use the second wire as a ground plane
But how to handheld rigs transmit and recieve with just one wire sticking in the air?
Your body acts as the ground when using a handheld radio. By holding the radio, you are capacitively coupled to the radio and make the other leg of the antenna. This is one of the reasons to hold the radio in your hand away from your body while using it, rather than using it while attached to a belt clip. (The other reasons pertain to RF safety.)
Of course, you aren't a very good ground system, so you can improve the efficiency of a handheld's antenna by attaching a counterpoise to the radio to be a better ground. There is a product called a "rat tail" designed for this purpose, but you can easily homebrew your own by attaching any handy piece of wire about a quarter wavelength long to the radio's case.
As noted in a comment: further details about adding your own ground/counterpoise to an HT.
actually ground is relative. Antenna's don't need an earth ground to work, but they need a relative ground point which is usually the base of the antenna.
Also the reason you want to place an antenna away is for transmission purposes. But using vhf at low power there is no chance of RF burns. When looking at antenna lobe designs it's best to place a high powered antenna so that the lobe is not angled toward animals because RF can damage animal tissue.