The honey/love potion makes your Tamagotchi fall in love so it can marry really quickly (just takes a few connections). You don't have to use it unless you want a super-fast marriage.
First, you need to have two adult Tamagotchis of the opposite gender. Connect them without giving them the love potion first so they can get acquainted. Do this once or twice. Then give one of them the love potion. It will walk around in a daze on the screen with hearts all over the place. Connect this Tamagotchi to the other Tamagotchi and select "present" or "visit." The Tamagotchis will stand together on one screen and kiss like crazy. Then they will go home, and you will see in the friends list that they have 4 hearts friendship level for each other.
Connect the Tamagotchis again, and if they are old enough to marry, they will marry and have kids. If they are not old enough, wait a while and keep trying again.
It's not really necessary unless you only get a small amount of time with another Tamagotchi and they both need to get married fast.