The Catholic church has a number of figures in its hierarchy. Most people rarely deal with anyone other than the priest at their parish, or perhaps a nun. An archbishop is an individual with quite a bit of clout in the church and there are certain, accepted addresses that are expected should you be writing to, introducing or speaking to an Archbishop
In a less formal situation you may address an archbishop as such. For instance, a simple "Hello, Archbishop Johnson" would not be frowned upon.
You cannot go wrong by being too formal, though long titles can be cumbersome in conversation. In a face-to-face situation, the formal "your Excellency" is acceptable when addressing an archbishop.
If you are introducing an archbishop to someone else, or especially to a group, you would want to use the archbishop's full title: The Most Revered (full name), Archbishop of (place name).
When writing a letter, you can use any of the above salutations when addressing an archbishop. The formality that you use is best decided so that it will match the tone of the letter.