Instructions
Open the main menu and configure your party so that the Pokemon you want to check is in the lead spot.
Travel to Goldenrod City and find the Bike Shop. This is east of the Radio Tower, located behind the Pokemon Center.
Enter the house next to the Bike Shop. You'll find a woman living there.
Talk to the woman and she'll tell you about your lead Pokemon's happiness. If she says "It looks really happy! It must love you a lot," this means the Pokemon is at max friendship level and has at least 250 friendship points. If she says "I get the feeling that it really trusts you," this means your Pokemon is nearing max friendship with between 200 to 249 friendship points. If she tells you "It's friendly toward you. It looks sort of happy," then you've earned between 150 to 199 friendship points and still have to work to earn max friendship.
Switch another Pokemon to be the lead in your party and repeat the process to check his friendship level.