Avoid the summer months and be there as early as possible. Buses arrive around 10 in the morning. It gets hot and crowded, up to 1000 people each day.
Montserrat is famous for the Black Madonna. Even in March, you have to queue for half an hour or longer to see and touch her. At 1 p.m. you can listen to the Montserrat Boys Choir.
I took the train from Barcelona which takes almost an hour. Check the timetable first, one train each hour only. After arriving at the station, you have two options to get to the top: either the mountain train or the funicular. I bought a combined ticket in Barcelona for the metro, train and mountain train. Price is reasonable in my opinion.
Monks are running different stalls like a bakery, honey, goat cheese, liquor and typical souvenirs. There are a couple of hikes to discover the natural beauty of the mountains which I enjoyed a lot. Maps are provided at the information center. You can stay there overnight when it is quiet and peaceful. I recommend this day trip if you spend a week in Barcelona. You can also go by car; there are enough parking lots.
(Updated by When to be Where)