Well, you got group IA and IIA just right, they are +1 and +2, respectively. The next column is the transition elements, we'll skip those for now. The real group IIIA, you know Boron, Aluminum, Gallium are in fact 3+. It does get a bit more complicated than that, pretty rapidly however.
Group IVA (Carbon, Silicon, Germanium) tend to form covalent bonds instead of forming 4+ ions. But still, 4 bonds, for group IVA. After that, we go the other direction -- Nitrogen -3, Oxygen -2, the halogens -1. And then the noble gases, which have a complete octet, and don't form compounds (at least, not easily -- sorry, complexity again)
The transition metals may form more than one ion -- there is Iron +2 and +3 but we tell you what we mean, we call them ferrous and ferric respectively. So there you go, it starts to get tricky,so we tell you the charge. Just like for plumbous, plumbic, mercurous, mercuric -- you can look those up.
Chromium is exciting, it can be +1, +2, +3, +4, +5, or +6. Even more fun, these ions are each different colors. In fact, that's so many ions, chromic and chromous wasn't enough, and we started numbering the ions Cr(III)3+, Cr(IV)4+. Matter of fact, the -ous and -ic I bored you with up above are being phased out. Well, that's what they said in my high school days, but they're still using them.
So yeah, it is a lot lot to memorize, but there are plenty of hints along the way to help jog your memory.