Both of your Tamagotchis have to be adults, oposite Genders, and approximatly the same age in order to get married. If they are, then you can use the "Love Posion" at this time.

To use it, just press the "B" button when you scroll through your item list, and find the "Love Posion." Once you see your Tamagotchi dancing, with hearts surrounded on both sides, then that means that you can fall in love, at the time the hearts are around the Tama . Just connect with you buddie and they should fall in love, instantly!
You don't need to use the "Love Posion" on both of your tamagotchis, just one one of them
Once you are able to see
'four hearts' under the Tamagotchi you connected with, in your "Friends Booklet/List", that means that they are ready to get married. Just connect a few more times, and *Vola*!
//Tama-Love