Here are some common grammar mistakes that I have seen online lately. Unfortunately, some of these have been on major websites, where the person who made the mistake is being paid a salary to write.

These explanations below are quite simple; more thorough explanations can be found at a variety of educational websites.

Then vs. Than

"Then" indicates a sequence of events, or at that time.
"We went to dinner, and then we saw the movie."
"I will not be ready then. I will need to meet you later."

"Than" is used after a comparative adjective or adverb to indicate an unequal comparison.
"John is a better actor than he." (another common error is to say "him" instead of "he")
"This is larger than life."

There, Their, and They're

"There" refers to a specific place, point, or condition.
"The book is over there."
"So where do we go from there?"

"Their" is the possessive form of "they."
"Their team is better than ours."
"The students need their books."

"They're" is a contraction of "they are."
"Tim said that they're going to be late."

Your vs. You're

"Your" is the possessive form of "you."
"Your shoelace is untied."

"You're" is a contraction of "you are."
"You're my best friend."