Antihydrogen does not occur naturally and therefore must be manufactured by bringing together the necessary building blocks in a particle accelerator. Many transuranic elements are produced in a similar way.
Since the structure of the common hydrogen atom comprises one electron and one proton, it follows that the structure of the antihydrogen atom is made up of one positron and one antiproton.
In theory, antihydrogen, and therefore all antimatter atoms, should behave in exactly the same way as their ordinary-matter counterparts, i.e., they fall into gravity wells (fall to earth as opposed to moving away), form molecules, etc.
As of this writing, no organisation has successfully created enough antihydrogen to perform many experiments; however, the Antihydrogen Trap Collaboration (ATRAP) is a collaboration amongst scientific establishments with the aim of generating large quantities of antihydrogen so that further studies may be performed. Currently, the main problem is that the building-block particles move too quickly, and therefore either they or any antimatter atoms they form annihilate with the normal matter of the accellerator wall before many atoms or molecules are formed.
At least one molecule of antihydrogen (H2, (pronounced aitch-bar too; SAMPA representation: [eItS ba:r\\' tu:]) has been indirectly observed, and interestingly, so has a molecule of hydrogen-antihydrogen. The HH (pronounced aitch-aitch-bar; SAMPA representation: [eItS eItS ba:r\\']) molecule is short lived and could be considered the molecular equivalent of the subatomic particles known as pions. HH self-annihilates by, first, deterioration of the electron/positron shell, and next, mutual destruction of the proton and antiproton that attract one another. The Coulomb force is responsible for the electromagnetic attraction of the proton and antiproton.
When antihydrogen has finally been created in quantity, the next antimatter isotopes scheduled for creation should be antideuterium (D), antitritium (T), and antihelium (He).