A possessive never occurs with a verb. Last night, yesterday, today, this year, tomorrow, etc. These, however, are never used with an apostrophe. In most cases, the word in the possessive is followed by another noun. The only exceptions are business or restaurant names because the names that would be following are implied.
Possessives occur in the following situations.
The car's front tires are worn. Susan's sister won't be coming home for break. Michelle's honesty is baffling at times. My brother's pies are the best. Something that belongs to a certain time period Last year's fall fashions are completely out of date now.