[Borek]

I thought that Hydrogen was a diatomic molecule (is that even the right word?), like Oxygen. So I thought that those kinds of atoms always had a sub...number thing of 2 when they are alone in an equation or something like that.

...How off am I, exactly?

In this case - completely. There are diatomic molecules of some gases, but they are never stable when they become charged (unless they are in gaseous state, which - as I have already stated - is a rather exotic case for HS chemistry).

[english]

No student should ever have to memorize the periodic table, billnotgatez.

I tend to disagree. Perhaps that's not the best way of learning chemistry, but you can't cope with it if you don't remember lot's of things. How do you expect to know that cesium sulfate is Cs₂SO₄ without either remembering that Cs is alkali metal (thus +1) or it is +1 (which gives the same formula of sulfate, but doesn't help to suppose it will be rather weakly complexed, will have most of salts soluble, will have almost entirely ionic salts and so on).

In case you want to say "You can always check these things" my answer is - "you don't want to waste your life checking alkali metals valence, you better remember it right now"

Sure, sure definitely Borek.  Very important stuff.  It just all stick after a while.   

[Yggdrasil]

I thought that Hydrogen was a diatomic molecule (is that even the right word?), like Oxygen. So I thought that those kinds of atoms always had a sub...number thing of 2 when they are alone in an equation or something like that.

...How off am I, exactly?

Hydrogen ions and hydrogen molecules are two different chemical substances.  Hydgrogen molecules (H₂) make up a flamable gas.  Hydrogen ions (H⁺) are very common place in aqueous solution.  Adding or taking away electrons from chemicals can vastly change their properties.  Another example would be sodium.  Elemental Na is a shiny metal which reacts violently with water.  Ionic Na⁺, however, is a very inert ion present in common salts (like table salt) or in many aqueous solutions (in fact, the human body contains a lot of Na⁺ ions.

So, it is important to differentiate between elements in their elemental form and elements when they are either charged ions or in covalent compounds with other atoms.

[constant thinker]

Yggdrasil beat my to the difference between H⁺ and H₂.

I have to agree with the no one should have to memorize the periodic table. The thing is, when you practice these things, you shouldn't have to physically put effort into memorizing the periodic table. Things should just come second nature, and you automatically know what the charges are and the formulas for that matter. It's like driving a manual, at first you have to put a lot of thought into it, but then after awhile you don't even realize your foot pushing in the clutch, and your hand shifting the gears.

The periodic table though and a list of polyatomic ions are excellent reference tools for when you encounter something you don't use often.

A good thing to do though after you think you've finished writing an equation is to go back, and look at the charges to make sure everything is neutral. Then once you do that you balance it, and then double check to make sure you have the same number of each atom on each side.