The cheaper means of sport are, the more popular they become.
(This sentence is about the relationship between the cost of sports and their popularity. "The cheaper" is used as the comparative form, followed by "the more" to emphasize the increasing popularity.)
He got old, the more bad-tempered he became.
(This sentence describes a person's behavior as they age. "The older" is used to indicate the cause of the bad temper.)
Take these medicines, and you will feel better if you do.
(This is a conditional sentence with the "if" clause suggesting that taking the medicine will result in feeling better.)
Tom gets up early, or he will be late for school.
(This sentence uses a "conditional or" structure where the second clause expresses the consequence of not following the first part. "Will be" indicates future possibility.)

The cheaper the means of sport are, the more popular they become
The older he got, the more bad-tempered he became
If you take these medicines, you will feel better
If Tom doesn't get up early, he will be late for school