I've done graduate-level work in physics, so I hope I know what I'm talking about.
Antimatter 101:
Every elementary particle has an antiparticle, which is a sort-of mirror image of it. Antimatter might be called mirror matter. Some particles are their own antiparticles, like photons. Antimatter has positive mass, just as ordinary matter does.
The antiparticle of an electron is an antielectron or positron. As far as can be determined, it has the same mass, opposite electric charge, and otherwise identical properties to within some sign changes. The
Particle Data Group has some stuff on tests of matter-antimatter comparisons for various particles, and so far, they are consistent with an important symmetry called CPT. Electrons and positrons having different masses, magnetic moments, and some other such properties would violate CPT. But from the PDG's page on electrons, that's been tested to VERY high accuracy.
An antimatter counterpart of a macroscopic object would have identical macroscopic properties, as far as can be determined. There'd be a few differences in the weak interactions, like spin directions and "CP violation effects" in particles like kaons, but even there, no big difference.
Those 38 antihydrogen atoms were just like 38 ordinary hydrogen atoms, but with a positron and antiproton instead of an electron and proton. Physicists hope to make enough enough of them to be able to measure their spectra, to see if they are the same as ordinary-hydrogen spectra. Differences would violate CPT.
The antihydrogen atoms were contained by using their magnetic fields. Though electrically neutral, their electron and proton have built-in spins, which make built-in magnetic-dipole moments (electron's one ~ 700 * proton's one). This gives these hydrogen atoms magnetic moments, meaning that they can be moved around with magnetic fields.
If enough antihydrogen atoms are produced, they may combine to make antihydrogen molecules. They are even more difficult to manipulate, since their positrons will form antiparallel, spin-0 pairs, reducing their magnetic moments by a large factor. If their antiprotons' spins are also antiparallel, like the ground state of ordinary hydrogen molecules, then they have zero magnetic moment. However, hydrogen molecules are diamagnetic, repelling about 10
-5 of an external magnetic field. So it will still be possible to use magnetic fields to hold antihydrogen molecules.
It must be pointed out that production of antimatter is typically VERY inefficient. I tracked down some stuff on how particle-accelerator labs make positrons and antiprotons for use in their experiments.
For positrons, shoot an electron beam with an energy of about 250 MeV at a metal target. It will produce about 5*10[sup]-3[/sup] positrons per electron, or a relative efficiency of 5*10
-5.
For antiprotons, shoot a proton beam with an energy of about 120 GeV at a metal target. it will produce about 2.5*10[sup]-5[/sup] antiprotons per proton, or a relative efficiency of 4*10
-7.
This is relative to all the energy going into pair production, which means that only half the energy goes into positrons or antiprotons.
Sources:
SpringerLink - Hyperfine Interactions, Volume 44, Numbers 1-4 -- Positron production for particle accelerators - positrons
Build a (Virtual) Particle Accelerator - antiprotons
Accelerator operation is an additional source of inefficiency, and I haven't been able to find good numbers for that.