Monterrico is an up-and-coming destination in Guatemala. Therefore, it's easy to find transportation there through the many tourist offices in Antigua. For a private and direct minibus (or shuttle), the price should be about $10. Any less than that is a bargain, and any more, go ahead and move on the next agency. A word of caution: be sure that you talk with the tour agency before you buy your ticket. Monterrico is situated on an island, and there isn't a bus service to get you off the island any earlier than you'd like. Arrange, or at least be aware of, the times the return trips from Monterrico leave. Over the weekend, when Monterrico is very popular, it should be relatively easy to find a way back to Antigua, even if you pay a driver at the last minute to take you. But, during the week, it can be difficult to leave.
In my case, I arrived on a Sunday and was told there would only be transportation leaving again on Wednesday from the island. I became sick while there and couldn't leave the island, which ended up being a real problem since I had pneumonia and sat around for 2 days with a high fever without medicine. This sickness ended up cutting my entire trip short by 2 months. By the time I got back to Antigua, I was so sick, all I wanted to do was get home and get better. Obviously, it is probably rare to fall ill immediately after arriving in Monterrico, but since it's possible to get "stuck" there, as I did, arrange a return trip with your tour office and be aware of any other methods of transport available to you.