I was alerted to this trio of words by my daughter, although it is generally just the first two versions that get used incorrecctly. First, here are the words in question:

Buy: to purchase something
I am going to buy a new laptop this week.

Bye: a farewell, shortened from goodbye. (Originally written as ‘bye to show it is an abbreviation, it is generally written as bye now)
They said bye to everyone outside then left the party.

by: to be beside , close to or in support of; within a time frame; in an opinion or according to
The mother kept her child by her side in the park.
I need to finish this by Friday
It’s not a complete definition by a long way.

The prefix bi also sounds the same, but is used as the start of other words (e.g. bicycle, bicentenary, bifocals, binary).

 If none of the above helps you remember the difference, rember the u in buy matches the u in purchase.

P.S. I explained the past tense of buy (bought) as a Monday Meaning last year.