The wedding ceremony will begin with Maramal saying, 'Ah here's the blushing bride / proud groom now. Head back into the Temple of Mara and the wedding will begin. Wait 24 hours and leave the temple then wait for the objective 'Attend your wedding ceremony' to be displayed. In order to complete the event, you will now need to travel back to the Temple of Mara in Riften and arrange the event. If you say yes, you can then proceed to marriage. They will respond and ask if you are interested as well.
Even if a character is flagged as marriageable, the Radiant AI system may not allow you to marry said character even if you have completed their objective, so it's best to have at least one backup candidate. In order for this option to become available, you must complete their objective. When you approach an eligible NPC, they may mention the amulet you are wearing. Maramal can be found in the Temple of Mara, but will initially be found in the Bee and Barb. You will not be able to marry anyone until you have spoken to Maramal about marriage, even if you have already obtained an amulet from somewhere else. You receive one during the Book of Love quest, which you keep when completed. The simplest way is to head to the Riften Temple of Mara and buy one from Maramal for 200 gold, but they will also show up in random loot and at merchants.
There are several ways to obtain an Amulet of Mara.