That means that you use “I” when the word you are using is the subject of the sentence; use “me” when the word is an object:

I went to the store.

He went to the store with me. (“Me” is the object of the prepositon “with.”)

He and I went to the store.

Who’s there? It is I. (that’s a tricky one!)

Give it to me.

He wrote the song for Jean and me. (Lots of people make a mistake on this one.)

Happier is correct. When to use “more” is very tricky, and you may have to just memorize when which words use that form. For instance, “happy” has fewer than three syllables, and the form is “happier.” But “full” is also fewer than 3 syllables, and I would say, “This closet is more full than the other one.” I can’t think of any word that ends in “y” that uses “more.”

Pretty = prettier

Happy = happier

Handsome = more handsome

Rich = richer

Wealthy = wealthier

Beautiful = more beautiful

restful = more restful

“me” is an object – that is, the person who gets the giving. This is a very simplied explanation. At this stage, just put the word in a phrase and see if it sounds right. “You pushed I” and “Me thinks so” obviously don’t.

If it is three or more syllables, use “more”.

For happy (two syllables), ‘happier’ would be correct.