[yuriyuri]

この、その、あの (kono, sono, ano) - Used with something after it
このペンは僕のだ。 (kono pen ha boku no da) - This pen is mine.

これ、それ、あれ (kore, sore, are) - Stand-alone
これはペンだ。(kore ha pen da) - This is a pen

And yes, spelling is as simple as that. The only things that you have to be careful of when it comes to spelling are a few exceptions for particles.

For example the most common mistake being the particle wa.
In romaji it is normally written as 'wa' because that is how it is pronounced, but it should be spelled with the hiragana for 'ha' (は)

Which is why you should try to not use romaji at all if you can help it, since it will just lead to confusion later on.

But from your post it sounds like you are taking a class, so if it is any good they will tell you this stuff anyway (That is assuming it isn't one of those classes that stays on romaji for years on end.)