Capital

"Capital" refers a city that is the seat of government for its region or is important in some way. 

It has other meanings, too. A capital is an uppercase letter. Capital is wealth or money, especially in the context of business:

Squiggly needs capital to get his hot chocolate stand up and running.

"Capital" can also mean “particular or significant”:

It is of capital importance that we arrive early so don’t end up in the back.

And it can mean “fabulous”:

Bringing songs to sing on the bus? That's a capital idea!

And of course, we have capital crimes and capital punishment, which relate to the death penalty.

Capitol

The other kind of "capitol" refers to buildings—state capitol buildings or, in the United States, the Capitol building in Washington, D.C. 

Since capitol with an O is just for buildings, think of the big rotunda of the Capitol building as round like the letter O in the word.

"Capitol" with an O refers only to buildings; that’s its only use. You can remember the spelling by thinking that the big rotunda of the Capitol building is round like the letter O in the word.

Should you capitalize 'capitol'?

You capitalize it when you’re writing about the Capitol building in D.C. where Congress meets. According to AP style, you should also capitalize it when referring to a specific state capitol building, but other style guides say to keep it lowercase for state capitol buildings, so be sure to check your style guide if you follow one.

The Senate convened at the Capitol to vote on the new bill.

Our class visited Wisconsin's Capitol in Madison last week. (AP style, NYT style)

Our class visited Wisconsin's capitol in Madison last week. (Chicago style)