The marital contract is the Nikah and no Islamic marriage is valid without it.
There are no set rules for how to do this, it can be a small affair a week before part 2 (explained) or on the same day as the Walima. It all begins with Islamic courting and ends with a wedding party.
Part 2: The big party afterwards is a public announcement known as the Walima, catered and sponsored by the husband. It's not supposed to be costly but it is supposed to be joyous and open to all.
Of course anyone else who is looking to settle down will have that in common with Muslims.
All this while though there is still no secret balcony meeting or physical contact allowed which is why the Nikah (Islamic marriage) needs to be performed first.
It's cultural customs that prolong or cut-short engagement periods. Part 1: Lastly, the couple get married by verbally accepting and signing a contract stating that they are a committed wife and husband in God's name and with His blessings.
You don't wait 6 months to get married and there is no gigantic engagement party.
But that's not to say you can't have an engagement party.